{"id":223864,"date":"2026-05-05T10:23:16","date_gmt":"2026-05-05T04:53:16","guid":{"rendered":"https:\/\/www.oliveboard.in\/blog\/?p=223864"},"modified":"2026-05-05T10:23:19","modified_gmt":"2026-05-05T04:53:19","slug":"surds-and-indices","status":"publish","type":"post","link":"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/","title":{"rendered":"Surds and Indices Question Types, Formulas, and Short Tricks"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_77 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of content<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#Download_Surds_and_Indices_Questions_PDF\" >Download Surds and Indices Questions PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#Practice_Surds_and_Indices_Questions_Live\" >Practice Surds and Indices Questions Live<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#Sign_Up\" >Sign Up<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#Login\" >Login<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#Forgot_Password\" >Forgot Password<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#i\" >&nbsp;<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#What_is_Surds_and_Indices_in_Quantitative_Aptitude\" >What is Surds and Indices in Quantitative Aptitude?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#Why_Is_Surds_and_Indices_Important_in_Competitive_Exams\" >Why Is Surds and Indices Important in Competitive Exams?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#Surds_and_Indices_Quantitative_Aptitude_Short_Notes\" >Surds and Indices Quantitative Aptitude Short Notes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#Surds_and_Indices_Revision_Summary\" >Surds and Indices Revision Summary<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#What_Are_the_Types_of_Surds_and_Indices_Questions_in_Quantitative_Aptitude\" >What Are the Types of Surds and Indices Questions in Quantitative Aptitude?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#Surds_and_Indices_Formulas_for_Quantitative_Aptitude\" >Surds and Indices Formulas for Quantitative Aptitude<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#Surds_and_Indices_Tricks_for_SSC_CGL_and_Other_Exams\" >Surds and Indices Tricks for SSC CGL and Other Exams<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#Surds_and_Indices_Concepts_for_Bank_Exams\" >Surds and Indices Concepts for Bank Exams<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#Common_Mistakes_to_Avoid_while_Solving_Surds_and_Indices\" >Common Mistakes to Avoid while Solving Surds and Indices<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#FAQs\" >FAQs<\/a><\/li><\/ul><\/nav><\/div>\n\n<p>Surds and Indices is one of the most important foundational topics in Quantitative Aptitude. Whether you&#8217;re preparing for SSC CGL, IBPS PO, SBI Clerk, RRB NTPC, or State PCS exams, this chapter can significantly boost your accuracy in number-based and algebraic calculations. In this blog, we have provided all the details about Surds and Indices meaning, along with concise short notes and key definitions to strengthen your basics along time-saving tricks, and fully solved questions based on the 20265 exam pattern.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Download_Surds_and_Indices_Questions_PDF\"><\/span>Download Surds and Indices Questions PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Download this concise PDF to quickly revise all key concepts of Surds and Indices, including laws of exponents, simplification techniques, rationalization methods, shortcut tricks, and exam-oriented MCQs with detailed solutions. It\u2019s a handy resource for <a href=\"https:\/\/www.oliveboard.in\/ssc-exams\/?ref=contmk-blog-pacq\" target=\"_blank\" rel=\"noreferrer noopener\">SSC<\/a>,\u00a0<a href=\"https:\/\/www.oliveboard.in\/railway-exams\/?ref=contmk-blog-pacq\" target=\"_blank\" rel=\"noreferrer noopener\">Railways<\/a> exams to help you practice efficiently and improve your problem-solving speed.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/www.oliveboard.in\/surds-and-indices-questions-pdf\/?ref=contmk-blog-saiq\" target=\"_blank\" rel=\"noreferrer noopener\">Download PDF<\/a><\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-practice-surds-and-indices-questions-live\"><span class=\"ez-toc-section\" id=\"Practice_Surds_and_Indices_Questions_Live\"><\/span><strong>Practice Surds and Indices Questions Live<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>In the following questions, you will find multiple-choice problems based on Surds and Indices concepts. Select the correct answer from the given options. Practicing a variety of such questions is essential to strengthen your understanding of powers, roots, and simplification techniques, improve speed, and enhance accuracy, ultimately helping you score better in competitive exams.<\/p>\n\n\n\n<!DOCTYPE html>\n<html lang=\"en\">\n<head>\n<meta charset=\"UTF-8\">\n<link rel=\"stylesheet\" href=\"https:\/\/courses.oliveboard.in\/edge\/css\/login-modal-for-blog.css\">\n\n<style>\n#quiz-1-sticky-header {\n  position: sticky;\n  top: 0;\n  z-index: 100;\n  background: #1565c0;\n  color: #fff;\n  padding: 12px 20px;\n  border-radius: 10px 10px 0 0;\n  display: flex;\n  justify-content: space-between;\n  align-items: center;\n  font-size: 16px;\n  font-weight: bold;\n  box-shadow: 0 2px 8px rgba(0,0,0,0.2);\n  margin: -20px -20px 20px -20px;\n}\n\n#quiz-1-score-badge {\n  background: rgba(255,255,255,0.2);\n  padding: 4px 12px;\n  border-radius: 20px;\n  font-size: 15px;\n  white-space: nowrap;\n}\n#quiz-1 * { box-sizing: border-box; }\n\n#quiz-1 .quiz-container {\n  max-width: 700px;\n  margin: auto;\n  padding: 20px;\n  background: #fff;\n  border-radius: 14px;\n  box-shadow: 0 6px 16px rgba(0,0,0,0.12);\n}\n\n#quiz-1 h2 {\n  text-align: center;\n}\n\n#quiz-1 .question {\n  margin-bottom: 22px;\n}\n\n#quiz-1 .question p {\n  font-weight: bold;\n}\n\n#quiz-1 button {\n  width: 100%;\n  padding: 12px;\n  margin: 6px 0;\n  border: none;\n  border-radius: 6px;\n  background: #e0e0e0;\n  color: #000;\n  font-size: 16px;\n  cursor: pointer;\n}\n\n#quiz-1 button:hover {\n  background: #d5d5d5;\n}\n\n#quiz-1 button.correct {\n  background: #4caf50;\n  color: #000;\n}\n\n#quiz-1 button.wrong {\n  background: #f44336;\n  color: #000;\n}\n\n#quiz-1 button.locked {\n  pointer-events: none;\n}\n\n\/* SUMMARY *\/\n#quiz-1 .final-summary {\n  margin-top: 40px;\n  padding: 20px;\n  border-radius: 14px;\n  background: #fafafa;\n  border: 2px solid #4caf50;\n}\n\n#quiz-1 .final-summary h3 {\n  text-align: center;\n  margin-bottom: 20px;\n}\n\n#quiz-1 .summary-row {\n  display: grid;\n  grid-template-columns: 120px 1fr 40px;\n  gap: 10px;\n  align-items: center;\n  margin-bottom: 12px;\n  font-weight: bold;\n}\n\n#quiz-1 .summary-bar {\n  height: 14px;\n  background: #ddd;\n  border-radius: 10px;\n  overflow: hidden;\n}\n\n#quiz-1 .bar-fill {\n  height: 100%;\n  width: 0%;\n}\n\n#quiz-1 .bar-attempted { background: #2196f3; }\n#quiz-1 .bar-correct { background: #4caf50; }\n#quiz-1 .bar-wrong { background: #f44336; }\n#quiz-1 .bar-unattempted { background: #9e9e9e; width: 100%; }\n\n#quiz-1 .final-score {\n  text-align: center;\n  font-size: 22px;\n  margin-top: 20px;\n}\n\n#quiz-1 .score-value {\n  font-size: 30px;\n  margin-left: 8px;\n}\n<\/style>\n<\/head>\n\n<body>\n<div id=\"quiz-1\">\n  <div class=\"quiz-container\">\n<div id=\"quiz-1-sticky-header\">\n  <span> Error Spotting Questions <\/span>\n  <span id=\"quiz-1-score-badge\">Score: <strong id=\"quiz-1-score-value\">0.00<\/strong><\/span>\n<\/div>\n\n    <!-- QUESTIONS -->\n\n<div class=\"question\" data-answered=\"false\">\n  <p>Q1) Simplify: \u221a75 + \u221a48 \u2212 \u221a27<\/p>\n  <button data-correct=\"false\">A. 4\u221a3<\/button>\n  <button data-correct=\"false\">B. 5\u221a3<\/button>\n  <button data-correct=\"true\">C. 6\u221a3<\/button>\n  <button data-correct=\"false\">D. 3\u221a3<\/button>\n<\/div>\n\n<div class=\"question\" data-answered=\"false\">\n  <p>Q2) If 2^x = 32, find x<\/p>\n  <button data-correct=\"false\">A. 4<\/button>\n  <button data-correct=\"true\">B. 5<\/button>\n  <button data-correct=\"false\">C. 6<\/button>\n  <button data-correct=\"false\">D. 3<\/button>\n<\/div>\n\n<div class=\"question\" data-answered=\"false\">\n  <p>Q3) Simplify: (\u221a5 + \u221a3)\u00b2<\/p>\n  <button data-correct=\"true\">A. 8 + 2\u221a15<\/button>\n  <button data-correct=\"false\">B. 8 \u2212 2\u221a15<\/button>\n  <button data-correct=\"false\">C. 6 + 2\u221a15<\/button>\n  <button data-correct=\"false\">D. 10 + 2\u221a15<\/button>\n<\/div>\n\n<div class=\"question\" data-answered=\"false\">\n  <p>Q4) If 9^x = 27, find x<\/p>\n  <button data-correct=\"true\">A. 3\/2<\/button>\n  <button data-correct=\"false\">B. 2\/3<\/button>\n  <button data-correct=\"false\">C. 1\/2<\/button>\n  <button data-correct=\"false\">D. 3\/4<\/button>\n<\/div>\n\n<div class=\"question\" data-answered=\"false\">\n  <p>Q5) Rationalize the denominator: 1\/(\u221a7 \u2212 \u221a5)<\/p>\n  <button data-correct=\"true\">A. (\u221a7 + \u221a5)\/2<\/button>\n  <button data-correct=\"false\">B. (\u221a7 \u2212 \u221a5)\/2<\/button>\n  <button data-correct=\"false\">C. (\u221a7 + \u221a5)\/4<\/button>\n  <button data-correct=\"false\">D. (\u221a5 + \u221a7)\/3<\/button>\n<\/div>\n\n<div class=\"question\" data-answered=\"false\">\n  <p>Q6) Find the value of (243)^(3\/5)<\/p>\n  <button data-correct=\"true\">A. 27<\/button>\n  <button data-correct=\"false\">B. 9<\/button>\n  <button data-correct=\"false\">C. 81<\/button>\n  <button data-correct=\"false\">D. 18<\/button>\n<\/div>\n\n<div class=\"question\" data-answered=\"false\">\n  <p>Q7) Simplify: (\u221a2 + \u221a3)(\u221a2 \u2212 \u221a3)<\/p>\n  <button data-correct=\"true\">A. \u22121<\/button>\n  <button data-correct=\"false\">B. 1<\/button>\n  <button data-correct=\"false\">C. 5<\/button>\n  <button data-correct=\"false\">D. \u22125<\/button>\n<\/div>\n\n<div class=\"question\" data-answered=\"false\">\n  <p>Q8) If 4^x \u00d7 2^(x\u22121) = 128, find x<\/p>\n  <button data-correct=\"true\">A. 8\/3<\/button>\n  <button data-correct=\"false\">B. 2<\/button>\n  <button data-correct=\"false\">C. 3<\/button>\n  <button data-correct=\"false\">D. 7\/3<\/button>\n<\/div>\n\n<div class=\"question\" data-answered=\"false\">\n  <p>Q9) Simplify: \u221a108 \u2212 \u221a75 + \u221a27<\/p>\n  <button data-correct=\"false\">A. 2\u221a3<\/button>\n  <button data-correct=\"false\">B. 3\u221a3<\/button>\n  <button data-correct=\"true\">C. 4\u221a3<\/button>\n  <button data-correct=\"false\">D. \u221a3<\/button>\n<\/div>\n\n<div class=\"question\" data-answered=\"false\">\n  <p>Q10) The value of (0.008)^(1\/3) is:<\/p>\n  <button data-correct=\"true\">A. 0.2<\/button>\n  <button data-correct=\"false\">B. 0.02<\/button>\n  <button data-correct=\"false\">C. 2<\/button>\n  <button data-correct=\"false\">D. 0.4<\/button>\n<\/div>\n\n<div class=\"question\" data-answered=\"false\">\n  <p>Q11) If x = 3 + 2\u221a2, find x + 1\/x<\/p>\n  <button data-correct=\"true\">A. 6<\/button>\n  <button data-correct=\"false\">B. 8<\/button>\n  <button data-correct=\"false\">C. 4<\/button>\n  <button data-correct=\"false\">D. 5<\/button>\n<\/div>\n\n<div class=\"question\" data-answered=\"false\">\n  <p>Q12) Simplify: (2^3 \u00d7 3^2)\/(2^2 \u00d7 3^3)<\/p>\n  <button data-correct=\"true\">A. 2\/3<\/button>\n  <button data-correct=\"false\">B. 3\/2<\/button>\n  <button data-correct=\"false\">C. 4\/9<\/button>\n  <button data-correct=\"false\">D. 9\/4<\/button>\n<\/div>\n\n<div class=\"question\" data-answered=\"false\">\n  <p>Q13) If \u221ax + \u221ay = \u221a(x+y), which condition must hold?<\/p>\n  <button data-correct=\"true\">A. xy = 0<\/button>\n  <button data-correct=\"false\">B. x = y<\/button>\n  <button data-correct=\"false\">C. x + y = 1<\/button>\n  <button data-correct=\"false\">D. x\/y = 1<\/button>\n<\/div>\n\n<div class=\"question\" data-answered=\"false\">\n  <p>Q14) Find the value of (32)^(-2\/5)<\/p>\n  <button data-correct=\"true\">A. 1\/4<\/button>\n  <button data-correct=\"false\">B. 4<\/button>\n  <button data-correct=\"false\">C. 1\/8<\/button>\n  <button data-correct=\"false\">D. 8<\/button>\n<\/div>\n\n<div class=\"question\" data-answered=\"false\">\n  <p>Q15) Simplify: \u221a(\u221a(\u221a256))<\/p>\n  <button data-correct=\"true\">A. 2<\/button>\n  <button data-correct=\"false\">B. 4<\/button>\n  <button data-correct=\"false\">C. 8<\/button>\n  <button data-correct=\"false\">D. 16<\/button>\n<\/div>\n\n    <!-- FINAL SUMMARY -->\n    <div class=\"final-summary\">\n      <h3>Quiz Summary <\/h3>\n\n      <div class=\"summary-row\">\n        <span>Attempted<\/span>\n        <div class=\"summary-bar\"><div class=\"bar-fill bar-attempted\" data-summary=\"attempted\"><\/div><\/div>\n        <span data-count=\"attempted\">0<\/span>\n      <\/div>\n\n      <div class=\"summary-row\">\n        <span>Correct<\/span>\n        <div class=\"summary-bar\"><div class=\"bar-fill bar-correct\" data-summary=\"correct\"><\/div><\/div>\n        <span data-count=\"correct\">0<\/span>\n      <\/div>\n\n      <div class=\"summary-row\">\n        <span>Wrong<\/span>\n        <div class=\"summary-bar\"><div class=\"bar-fill bar-wrong\" data-summary=\"wrong\"><\/div><\/div>\n        <span data-count=\"wrong\">0<\/span>\n      <\/div>\n\n      <div class=\"summary-row\">\n        <span>Unattempted<\/span>\n        <div class=\"summary-bar\"><div class=\"bar-fill bar-unattempted\" data-summary=\"unattempted\"><\/div><\/div>\n        <span data-count=\"unattempted\">0<\/span>\n      <\/div>\n\n      <div class=\"final-score\">\n        Final Score: <span class=\"score-value\" data-score>0.0<\/span>\n      <\/div>\n    <\/div>\n\n  <\/div>\n<\/div>\n<div class=\"modal modal-obls\" id=\"modal-signup\">\n        <div class=\"modal-background\"><\/div>\n        <div class=\"modal-content\">\n           <div class=\"obls-group\" id=\"obls-group1\">\n               <div class=\"obls-blk\">\n                   <span class=\"img-box\"><img decoding=\"async\" src=\"\/img\/img-delivery.svg\" alt=\"\"><\/span>\n                   <h2 id=\"display-register-text\"><span class=\"ez-toc-section\" 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\u00d7 a&lt;sup&gt;n&lt;\/sup&gt;<\/td><td>= a&lt;sup&gt;m+n&lt;\/sup&gt;<\/td><\/tr><tr><td>(a&lt;sup&gt;m&lt;\/sup&gt;)&lt;sup&gt;n&lt;\/sup&gt;<\/td><td>= a&lt;sup&gt;m\u00d7n&lt;\/sup&gt;<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-surds-and-indices-revision-summary\"><span class=\"ez-toc-section\" id=\"Surds_and_Indices_Revision_Summary\"><\/span>Surds and Indices Revision Summary<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Concepts used to solve surds and indices questions are as follows:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Concept<\/strong><\/td><td><strong>Explanation<\/strong><\/td><\/tr><tr><td>Laws of Indices \u2013 Rule 1<\/td><td>a&lt;sup&gt;m&lt;\/sup&gt; \u00d7 a&lt;sup&gt;n&lt;\/sup&gt; = a&lt;sup&gt;m+n&lt;\/sup&gt;<\/td><\/tr><tr><td>Laws of Indices \u2013 Rule 2<\/td><td>(a&lt;sup&gt;m&lt;\/sup&gt;)&lt;sup&gt;n&lt;\/sup&gt; = a&lt;sup&gt;m\u00d7n&lt;\/sup&gt;<\/td><\/tr><tr><td>Product of Surds<\/td><td>\u221aa \u00d7 \u221ab = \u221a(a\u00d7b)<\/td><\/tr><tr><td>Division of Surds<\/td><td>\u221aa \/ \u221ab = \u221a(a \/ b)<\/td><\/tr><tr><td>Conjugate of Binomial Surd<\/td><td>(\u221aa + \u221ab)(\u221aa &#8211; \u221ab) = a &#8211; b<\/td><\/tr><tr><td>Surd Rationalization<\/td><td>Multiply by conjugate to remove surd from denominator<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-what-are-the-types-of-surds-and-indices-questions-in-quantitative-aptitude\"><span class=\"ez-toc-section\" id=\"What_Are_the_Types_of_Surds_and_Indices_Questions_in_Quantitative_Aptitude\"><\/span>What Are the Types of Surds and Indices Questions in Quantitative Aptitude?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Surds and Indices questions are mostly formula-based but can also include mixed-type logic. <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Direct Simplification:<\/strong> Based on laws of indices\/surds<\/li>\n\n\n\n<li><strong>Nested Roots:<\/strong> Questions like \u221a(5 + \u221a6)<\/li>\n\n\n\n<li><strong>Rationalization:<\/strong> Removing surd from denominator<\/li>\n\n\n\n<li><strong>Word Problems:<\/strong> Combining exponent logic with real-life scenarios<\/li>\n\n\n\n<li><strong>Mixed Algebraic Expressions:<\/strong> Indices in equations<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/www.oliveboard.in\/sbi-po-mock-test\/?ref=contac-acb\" target=\"_blank\" rel=\"noreferrer noopener\">Attempt A Free SBI PO Mock Test<\/a><\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-surds-and-indices-formulas-for-quantitative-aptitude\"><span class=\"ez-toc-section\" id=\"Surds_and_Indices_Formulas_for_Quantitative_Aptitude\"><\/span>Surds and Indices Formulas for Quantitative Aptitude<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>To solve quickly and accurately, memorize the following formulas:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a&lt;sup>m&lt;\/sup> \u00d7 a&lt;sup>n&lt;\/sup> = a&lt;sup>m+n&lt;\/sup><\/li>\n\n\n\n<li>a&lt;sup>m&lt;\/sup> \u00f7 a&lt;sup>n&lt;\/sup> = a&lt;sup>m\u2212n&lt;\/sup><\/li>\n\n\n\n<li>(a&lt;sup>m&lt;\/sup>)&lt;sup>n&lt;\/sup> = a&lt;sup>mn&lt;\/sup><\/li>\n\n\n\n<li>(ab)&lt;sup>n&lt;\/sup> = a&lt;sup>n&lt;\/sup> \u00d7 b&lt;sup>n&lt;\/sup><\/li>\n\n\n\n<li>(a\/b)&lt;sup>n&lt;\/sup> = a&lt;sup>n&lt;\/sup> \/ b&lt;sup>n&lt;\/sup><\/li>\n\n\n\n<li>Rationalizing denominator: 1 \/ (\u221aa + \u221ab) = (\u221aa \u2212 \u221ab)\/(a \u2212 b)<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-surds-and-indices-tricks-for-ssc-cgl-and-other-exams\"><span class=\"ez-toc-section\" id=\"Surds_and_Indices_Tricks_for_SSC_CGL_and_Other_Exams\"><\/span>Surds and Indices Tricks for SSC CGL and Other Exams<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Time-saving tricks to solve Surds and Indices questions are as follows:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Convert surds to single root where possible<\/li>\n\n\n\n<li>Use exponent laws when simplifying big powers<\/li>\n\n\n\n<li>Conjugate multiplication helps remove surds from denominators<\/li>\n\n\n\n<li>Break powers into base units like a&lt;sup>2n&lt;\/sup><\/li>\n\n\n\n<li>Use approximation: \u221a2 \u2248 1.414, \u221a3 \u2248 1.732 when needed<\/li>\n\n\n\n<li>Memorize \u221a1 to \u221a25 for quick identification<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-surds-and-indices-concepts-for-bank-exams\"><span class=\"ez-toc-section\" id=\"Surds_and_Indices_Concepts_for_Bank_Exams\"><\/span>Surds and Indices Concepts for Bank Exams<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Bank exams like <strong>IBPS PO<\/strong> and <strong>SBI PO<\/strong> may twist Surds &amp; Indices into logic-based puzzles or combine them with inequalities and data interpretation.<\/p>\n\n\n\n<p><strong>Example:<\/strong><br>If 2&lt;sup&gt;2x&lt;\/sup&gt; = 16, then x = ?<br>Solution: 2&lt;sup&gt;2x&lt;\/sup&gt; = 2&lt;sup&gt;4&lt;\/sup&gt; \u21d2 2x = 4 \u21d2 <strong>x = 2<\/strong><\/p>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/www.oliveboard.in\/ibps-po-mock-test\/?ref=contac-acb\" target=\"_blank\" rel=\"noreferrer noopener\">Attempt A Free IBPS PO Mock Test<\/a><\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-common-mistakes-to-avoid-while-solving-surds-and-indices\"><span class=\"ez-toc-section\" id=\"Common_Mistakes_to_Avoid_while_Solving_Surds_and_Indices\"><\/span>Common Mistakes to Avoid while Solving Surds and Indices<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>While solving Surds and Indices Quantitative Aptitude questions candidates must keep the below mentioned details in mind:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Confusing Surd and Rational Numbers:<\/strong> Always check if a number is completely simplified (e.g., \u221a8 = 2\u221a2, not irrational in its raw form).<\/li>\n\n\n\n<li><strong>Ignoring Index Laws:<\/strong> Apply correct power laws while multiplying or dividing (e.g., a^m \u00d7 a^n = a^(m+n), not a^(mn)).<\/li>\n\n\n\n<li><strong>Wrong Rationalization:<\/strong> Always multiply by the conjugate, not the same expression (e.g., rationalize 1\/(\u221a2 + 1) using \u221a2 \u2212 1).<\/li>\n\n\n\n<li><strong>Incorrect Root Values:<\/strong> Avoid approximating without simplification (e.g., \u221a20 \u2260 4; correct form is \u221a(4\u00d75) = 2\u221a5).<\/li>\n\n\n\n<li><strong>Not Breaking Powers Properly:<\/strong> a^6 \u2260 a^2 \u00d7 3; remember it\u2019s (a^2)^3 = a^(2\u00d73), not multiplication of base and index.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-faqs\"><span class=\"ez-toc-section\" id=\"FAQs\"><\/span>FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<div class=\"schema-faq wp-block-yoast-faq-block\"><div class=\"schema-faq-section\" id=\"faq-question-1754573833610\"><strong class=\"schema-faq-question\"><strong>Q1. How to solve Surds and Indices questions fast?<\/strong><\/strong> <p class=\"schema-faq-answer\">Use index laws and surd simplification rules. Practice rationalizing frequently.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1754573834467\"><strong class=\"schema-faq-question\"><strong>Q2. Are Surds and Indices questions asked in SBI PO Mains?<\/strong><\/strong> <p class=\"schema-faq-answer\">Yes, especially in simplification or mixed DI sets.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1754573835121\"><strong class=\"schema-faq-question\"><strong>Q3. Can I skip Surds and Indices in SSC CGL Quantitative Aptitude?<\/strong><\/strong> <p class=\"schema-faq-answer\">Not advisable. It\u2019s an easy scoring topic with at least 1\u20132 questions.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1754573836002\"><strong class=\"schema-faq-question\"><strong>Q4. What are symbol-based Surds and Indices questions?<\/strong><\/strong> <p class=\"schema-faq-answer\">These may involve coded indices or substitutions like a = \u221a2, b = \u221a3 to test simplification.<\/p> <\/div> <\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n<ul class=\"wp-block-latest-posts__list is-grid columns-3 wp-block-latest-posts\"><li><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/www.oliveboard.in\/blog\/ibps-po-prelims-pyps\/\">IBPS PO Previous Year Papers, 2025-2020 PYPs, Download PDF<\/a><\/li>\n<li><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/www.oliveboard.in\/blog\/rrb-ntpc-pyps\/\">RRB NTPC 2025 Question Papers, Shift-Wise PYPs, Download PDFs<\/a><\/li>\n<li><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/www.oliveboard.in\/blog\/ssc-chsl-reasoning-questions\/\">SSC CHSL Reasoning Questions, Download PDF &amp; Attempt Live Quiz<\/a><\/li>\n<li><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/www.oliveboard.in\/blog\/ssc-stenographer-english-questions\/\">SSC Stenographer English Questions, Attempt Live Quiz<\/a><\/li>\n<li><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/www.oliveboard.in\/blog\/ssc-cgl-english-questions\/\">SSC CGL English Questions with Answers, Download Free PDF<\/a><\/li>\n<li><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/www.oliveboard.in\/blog\/ssc-chsl-full-form\/\">SSC CHSL Full Form, All you need to know about SSC CHSL Exam<\/a><\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"<p>Surds and Indices is one of the most important foundational topics in Quantitative Aptitude. Whether you&#8217;re preparing for SSC CGL,<\/p>\n","protected":false},"author":58,"featured_media":243470,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[31,10231],"tags":[],"class_list":["post-223864","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-bank-exams","category-ssc-railways","generate-columns","tablet-grid-50","mobile-grid-100","grid-parent","grid-50"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v26.6 (Yoast SEO v26.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Surds and Indices Question Types, Formulas, and Short Tricks<\/title>\n<meta name=\"description\" content=\"Check out the detailed formulas used to solve Surds and Indices questions, along with concepts and time-saving short tricks and tips.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Surds and Indices Question Types, Formulas, and Short Tricks\" \/>\n<meta property=\"og:description\" content=\"Surds and Indices is one of the most important foundational topics in Quantitative Aptitude. 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I work as a Content Writer at Oliveboard, where I have been simplifying exam-related content for the past 4 years. I create clear and easy-to-understand guides for JAIIB, CAIIB, and UGC exams. My work includes breaking down notifications, admit cards, and exam updates, as well as preparing study plans and subject-wise strategies. My goal is to support working professionals in managing their exam preparation alongside a full-time job and to help them achieve career growth.\",\"sameAs\":[\"www.linkedin.com\/in\/aditi-chakraborty-131b3b379\"]},{\"@type\":\"Question\",\"@id\":\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#faq-question-1754573833610\",\"position\":1,\"url\":\"https:\/\/www.oliveboard.in\/blog\/surds-and-indices\/#faq-question-1754573833610\",\"name\":\"Q1. How to solve Surds and Indices questions fast?\",\"answerCount\":1,\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Use index laws and surd simplification rules. 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