Railways Notes / Mathematics (Quantitative Aptitude) / Chapter 26
Chapter 26 of 31

Surds and Indices

The laws of exponents and simplification rules for surds — used constantly in Simplification and Algebra questions.

📖 ~4 min read 📐 RRB NTPC / Group D — Mathematics

Laws of Indices

LawRule
Product ruleaᵐ × aⁿ = aᵐ⁺ⁿ
Quotient ruleaᵐ ÷ aⁿ = aᵐ⁻ⁿ
Power of a power(aᵐ)ⁿ = aᵐⁿ
Negative exponenta⁻ⁿ = 1/aⁿ
Zero exponenta⁰ = 1 (a ≠ 0)
Fractional exponenta^(1/n) = ⁿ√a

Surds

  • A surd is an irrational root that cannot be simplified to remove the root sign (e.g., √2, √3)
  • Like surds have the same number under the root (2√3 and 5√3) and can be added/subtracted directly
  • To simplify a surd, factor out the largest perfect square: √50 = √(25×2) = 5√2
💡 Example: Simplify 3√2 + 5√2 = 8√2 (like surds combine directly, like algebraic terms)

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