Apt Surds Indices — Free Aptitude Tutorial
Learn Apt Surds Indices in Aptitude with a free, beginner-friendly tutorial, examples and practice for Indian students on Syllab.in.
TL;DR: Learn Apt Surds Indices in Aptitude with a free, beginner-friendly tutorial, examples and practice for Indian students on Syllab.in.
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Apt Surds Indices in Aptitude
Indices (Exponents): aᵐ × aⁿ = aᵐ⁺ⁿ. aᵐ / aⁿ = aᵐ⁻ⁿ. (aᵐ)ⁿ = aᵐⁿ. a⁰ = 1. a⁻ⁿ = 1/aⁿ.
Surds: Irrational roots that cannot be simplified. √2, √3, ∛5 are surds. √4 = 2 (not a surd).
Rationalizing the denominator: Multiply by conjugate. 1/√2 = √2/2. 1/(√3+√2) = (√3−√2)/((√3)²−(√2)²) = √3−√2.
Laws of radicals: √(a×b) = √a×√b. √(a/b) = √a/√b. (√a)² = a.
Comparing surds: To compare √3 and ∛4, raise both to the power 6 (LCM of 2 and 3): 3³=27 vs 4²=16. So √3 > ∛4.
Apt Surds Indices — Syntax
aᵐ × aⁿ = aᵐ⁺ⁿ aᵐ / aⁿ = aᵐ⁻ⁿ (aᵐ)ⁿ = aᵐⁿ Rationalize: 1/(a+√b) × (a-√b)/(a-√b)
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