Surds and Indices Question Types, Formulas, and Short Tricks

Published on 7 August 2025 by

Surds and Indices is one of the most important foundational topics in Quantitative Aptitude. Whether you’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 2024–25 exam pattern.

What Is Surds and Indices in Quantitative Aptitude?

In Quantitative Aptitude, Indices refer to the powers or exponents applied to numbers, whereas Surds are irrational numbers that can’t be simplified into rational form but can be expressed using roots (√).

Why does it appear in exams?
Because this topic tests your understanding of roots, exponents, and algebraic simplificatio essential for solving higher-order equations and simplifications.

Skills required:

  • Understanding of number properties
  • Logical simplification
  • Pattern recognition
  • Basic algebra

Why Is Surds and Indices Important in Competitive Exams?

Understanding Surds and Indices helps in solving various simplification, number system, and algebraic problems accurately and quickly.

ExamNo. of QuestionsDifficulty
SSC CGL / CHSL1–2Easy
IBPS PO / SBI PO1–2Moderate
RRB NTPC / Group D1Easy
State PSC / Police1–2Moderate
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Surds and Indices Quantitative Aptitude Short Notes

The key concepts and definitions you need to remember while solving Surds and Indices problems in Quant:

TermExplanation
Index (Exponent)Represents how many times a number is multiplied
SurdAn irrational number with a root that cannot be simplified
√a × √b= √(a × b)
√a / √b= √(a / b)
a<sup>m</sup> × a<sup>n</sup>= a<sup>m+n</sup>
(a<sup>m</sup>)<sup>n</sup>= a<sup>m×n</sup>

Surds and Indices Revision Summary

Concepts used to solve surds and indices questions are as follows:

ConceptExplanation
Laws of Indices – Rule 1a<sup>m</sup> × a<sup>n</sup> = a<sup>m+n</sup>
Laws of Indices – Rule 2(a<sup>m</sup>)<sup>n</sup> = a<sup>m×n</sup>
Product of Surds√a × √b = √(a×b)
Division of Surds√a / √b = √(a / b)
Conjugate of Binomial Surd(√a + √b)(√a – √b) = a – b
Surd RationalizationMultiply by conjugate to remove surd from denominator

What Are the Types of Surds and Indices Questions in Quantitative Aptitude?

Surds and Indices questions are mostly formula-based but can also include mixed-type logic.

  • Direct Simplification: Based on laws of indices/surds
  • Nested Roots: Questions like √(5 + √6)
  • Rationalization: Removing surd from denominator
  • Word Problems: Combining exponent logic with real-life scenarios
  • Mixed Algebraic Expressions: Indices in equations
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Surds and Indices Formulas for Quantitative Aptitude

To solve quickly and accurately, memorize the following formulas:

  • a<sup>m</sup> × a<sup>n</sup> = a<sup>m+n</sup>
  • a<sup>m</sup> ÷ a<sup>n</sup> = a<sup>m−n</sup>
  • (a<sup>m</sup>)<sup>n</sup> = a<sup>mn</sup>
  • (ab)<sup>n</sup> = a<sup>n</sup> × b<sup>n</sup>
  • (a/b)<sup>n</sup> = a<sup>n</sup> / b<sup>n</sup>
  • Rationalizing denominator: 1 / (√a + √b) = (√a − √b)/(a − b)

Surds and Indices Tricks for SSC CGL and Other Exams

Time-saving tricks to solve Surds and Indices questions are as follows:

  1. Convert surds to single root where possible
  2. Use exponent laws when simplifying big powers
  3. Conjugate multiplication helps remove surds from denominators
  4. Break powers into base units like a<sup>2n</sup>
  5. Use approximation: √2 ≈ 1.414, √3 ≈ 1.732 when needed
  6. Memorize √1 to √25 for quick identification

Solved Surds and Indices Questions from 2024–25 Exams

Here are memory-based and mock-based recent questions:

Q1. (Asked in SSC CGL 2024 Tier 1 – Shift 2)
Simplify: √48 + √12
Answer: √48 = 4√3, √12 = 2√3 ⇒ 4√3 + 2√3 = 6√3

Q2. (From IBPS PO Prelims 2024 – Mock)
If a<sup>4</sup> = 81, find a
Answer: a = (81)<sup>1/4</sup> = (3<sup>4</sup>)<sup>1/4</sup> = 3

Q3. (Asked in RRB NTPC 2024 – Memory Based)
Simplify: (2√3 + 3√2)(2√3 − 3√2)
Answer: = (2√3)<sup>2</sup> − (3√2)<sup>2</sup> = 12 − 18 = −6

Surds and Indices Concepts for Bank Exams

Bank exams like IBPS PO and SBI PO may twist Surds & Indices into logic-based puzzles or combine them with inequalities and data interpretation.

Example:
If 2<sup>2x</sup> = 16, then x = ?
Solution: 2<sup>2x</sup> = 2<sup>4</sup> ⇒ 2x = 4 ⇒ x = 2

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Common Mistakes to Avoid while Solving Surds and Indices

While solving Surds and Indices Quantitative Aptitude questions candidates must keep the below mentioned details in mind:

  • Confusing Surd and Rational Numbers: Always check if a number is completely simplified (e.g., √8 = 2√2, not irrational in its raw form).
  • Ignoring Index Laws: Apply correct power laws while multiplying or dividing (e.g., a^m × a^n = a^(m+n), not a^(mn)).
  • Wrong Rationalization: Always multiply by the conjugate, not the same expression (e.g., rationalize 1/(√2 + 1) using √2 − 1).
  • Incorrect Root Values: Avoid approximating without simplification (e.g., √20 ≠ 4; correct form is √(4×5) = 2√5).
  • Not Breaking Powers Properly: a^6 ≠ a^2 × 3; remember it’s (a^2)^3 = a^(2×3), not multiplication of base and index.

FAQs

Q1. How to solve Surds and Indices questions fast?

Use index laws and surd simplification rules. Practice rationalizing frequently.

Q2. Are Surds and Indices questions asked in SBI PO Mains?

Yes, especially in simplification or mixed DI sets.

Q3. Can I skip Surds and Indices in SSC CGL Quantitative Aptitude?

Not advisable. It’s an easy scoring topic with at least 1–2 questions.

Q4. What are symbol-based Surds and Indices questions?

These may involve coded indices or substitutions like a = √2, b = √3 to test simplification.