What is the simplest rationalising factor of cubth root of 500

Cube root of 500 = cube root of (5 x 5 x 5 x 2 x 2) = 5 x cube root of (2 x 2) Hence to rationalize cube root of 500, we require another cube root of 2 i.e., 2 ...

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Standard IX

Mathematics

Introduction to Algebraic Identities

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What is the simplest rationalising factor of cube root of 500

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Solution

Cube root of 500
$(500)^{\frac{1}{3}}$
$= {\sqrt{(5 \times 100)}}^{\frac{1}{3}}$
$= {\sqrt{(2 \times 2 \times 5 \times 5 \times 5)}}^{\frac{1}{3}}$
$= 5 {\sqrt{4}}^{\frac{1}{3}}$
Hence rationalizing factor is $2^{\frac{1}{3}}$

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What is the simplest rationalising factor of cube root of 500

Cube root of 500(500)13 =√(5×100)13 =√(2×2×5×5×5)13 =5√413 Hence rationalizing factor is 213

Cube root of 500
$(500)^{\frac{1}{3}}$
$= {\sqrt{(5 \times 100)}}^{\frac{1}{3}}$
$= {\sqrt{(2 \times 2 \times 5 \times 5 \times 5)}}^{\frac{1}{3}}$
$= 5 {\sqrt{4}}^{\frac{1}{3}}$
Hence rationalizing factor is $2^{\frac{1}{3}}$