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Aptitude Topics

Surds & Indices

Surds and indices are important concepts in arithmetic and algebra. They help simplify roots, powers, exponential expressions, and complex calculations quickly.

Fundamental Principles

Index (Exponent)

An index or exponent indicates how many times a number is multiplied by itself.

Surd

A surd is an irrational root expression that cannot be simplified into a rational number.

Rationalization

The process of removing surds from the denominator of a fraction.

Essential Formulation Tips

  • Memorize the laws of indices before solving problems.
  • Convert roots into fractional exponents when possible.
  • Simplify surds by extracting perfect squares.
  • Always rationalize denominators containing surds.
  • Use exponent rules to simplify large expressions quickly.

Shortcut Execution Techniques

  • aᵐ × aⁿ = aᵐ⁺ⁿ
  • aᵐ ÷ aⁿ = aᵐ⁻ⁿ
  • (aᵐ)ⁿ = aᵐⁿ
  • √a = a¹ᐟ²
  • 1/(√a + √b) → Multiply numerator and denominator by (√a − √b)

Contextual Inquiries (FAQs)

Q: What is a surd?

A: An irrational root expression such as √2, √3, or √5.

Q: Why are indices important?

A: Indices simplify calculations involving repeated multiplication and powers.

Q: What is rationalization used for?

A: It removes surds from denominators and simplifies expressions.