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SBI Clerk Surds & Indices

Study Material — 7 PYQs (2020–2020) · Concept Notes · Shortcuts

SBI Clerk Surds & Indices is a frequently tested subtopic — 7 previous year questions from 2020–2020 papers are included below with concept notes, key rules and shortcut tricks.

7 PYQs
2020–2020
3 Practice
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6 Key Points
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Previous Year Questions

SBI Clerk Surds & Indices — Past Exam Questions

7 questions from actual SBI Clerk papers · all shown free · click option to reveal solution

Exam Q 12020Previous Year Pattern

Simplify: ∛(27) × ∜(16) ÷ √(4)

Exam Q 22020Previous Year Pattern

If √(x) = 5, find the value of x^(3/2).

Exam Q 32020Previous Year Pattern

If (2^a × 3^b × 5^c)^(1/3) = 2^2 × 3^(1/2) × 5^(1/3), then find the value of 2a + 3b + 6c.

Exam Q 42020Previous Year Pattern

Simplify: (√5 + √3)^2 / (√5 - √3) × (√5 + √3) / (√5 + √3)^2. What is the result?

Exam Q 52020Previous Year Pattern

If 3^(2x - 1) × 9^(x + 1) = 27^(x/3), find the value of x.

Exam Q 62020Previous Year Pattern

If 2^a = 3^b = 6^c, then express c in terms of a and b. What is the relationship?

Exam Q 72020Previous Year Pattern

Simplify: [∜(16) × ∛(27)] / [√(4)] + (32)^(2/5). What is the result?

Concept Notes

Surds & Indices— Rules & Concept

Core ConceptRead this first — the foundation of the topic
Index Laws

- a^m × a^n = a^(m+n) - a^m ÷ a^n = a^(m-n) - (a^m)^n = a^(mn) - a^0 = 1 (for any a ≠ 0) - a^(-n) = 1/a^n 2

Surd Rules

- √(a × b) = √a × √b - √(a/b) = √a / √b - (√a)^2 = a - √a × √a = a 3

Rationalizing Surds

Remove surds from the denominator by multiplying numerator and denominator by the conjugate. **

Formula BlockMemorise — at least one formula appears in every paper

a^(m/n) = ⁿ√(a^m) — This connects indices and surds. For example, 8^(2/3) = ³√(8²) = ³√64 = 4

Exam PatternsWhat examiners ask — read before attempting PYQs

SSC CGL usually asks: - Simplify expressions using index laws - Rationalize denominators containing surds - Convert between index and surd notation - Find unknown exponents in equations - Compare surd values SHORTCUT/TRICK: When rationalizing 1/(√a + √b), multiply by (√a - √b)/(√a - √b). This uses the difference of squares formula: (x+y)(x-y) = x² - y². The denominator becomes a - b instantly, removing all surds.

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Convert to surd form 16^(3/4) = ⁴√(16³) = (⁴√16)³ = 2³ = 8

2
Step 2

Simplify the denominator 8^(-2/3) = 1/(8^(2/3)) = 1/(³√(8²)) = 1/(³√64) = 1/4

3
Step 3

Divide 8 ÷ (1/4) = 8 × 4 = 32 **

Exam TrapsCommon mistakes students make — avoid these

** Students often forget that √a × √b ≠ √(a+b). The correct rule is √a × √b = √(ab). Also, many forget that a^(1/2) = √a, not a/2.

Key Points to Remember

  • Index law a^m × a^n = a^(m+n) works only when the base is the same
  • a^(m/n) = ⁿ√(a^m)—this is the bridge between indices and surds
  • Rationalizing means removing surds from the denominator using conjugate multiplication
  • √(ab) = √a × √b, but √(a+b) ≠ √a + √b—this is a critical trap
  • Any number to the power 0 equals 1: a^0 = 1 (except when a = 0)
  • Negative indices flip the fraction: a^(-n) = 1/a^n

Exam-Specific Tips

  • The general index law for multiplication is a^m × a^n = a^(m+n), valid for all real bases and exponents
  • The fractional index formula a^(m/n) = ⁿ√(a^m) allows conversion between power and root notation
  • A surd is an irrational root that cannot be expressed as a simple fraction (e.g., √2, √3, ∛7)
  • To rationalize 1/(√a + √b), multiply by (√a - √b)/(√a - √b) to eliminate surds from denominator
  • The law (a^m)^n = a^(mn) means nested powers multiply—critical for simplification questions
  • Any non-zero number raised to power 0 equals 1: a^0 = 1 (this is an axiomatic rule in SSC questions)
  • √a × √a = a for any positive real number a—this is used in rationalizing and simplifying
Practice MCQs

Surds & Indices — Practice Questions

3graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

Simplify: (3⁴ × 3⁻²) ÷ 3¹

Practice 2easy

Rationalize: 1/(√7 − √5)

Practice 3easy

If 2^(3x) = 512, find the value of x.

60-Second Revision — Surds & Indices

  • Remember: Index laws work only with the same base. Don't add exponents unless bases are identical.
  • Formula: a^(m/n) = ⁿ√(a^m)—use this to convert between exponent and root forms instantly.
  • Trap: √(a+b) ≠ √a + √b. This is a very common error. Only √(ab) = √a × √b is valid.
  • Rationalizing trick: For 1/(√a + √b), multiply top and bottom by (√a - √b) to use difference of squares.
  • Key rule: a^0 = 1 and a^(-n) = 1/a^n—these appear in almost every SSC surd question.
  • Practice step: Always convert surds to index form first, simplify using index laws, then convert back if needed.
  • Check: After simplifying, verify your answer makes sense—surds should reduce, and fractions should simplify completely.
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