√( 27/125)=√( 1 × 27)/√(125) = √(( 1) × ( 1) × ( 1)× 3 × 3 × 3)/√(5× 5 × 5) =√(( 1)^3 × 3^3)/√(5^3)= 1 × 3/5 = 3/5 ...

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Cube Root Using Prime Factorisation

Evaluate : √-...

Question

Evaluate :
$\sqrt[3]{\frac{- 27}{125}}$

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Solution

$\sqrt[3]{\frac{- 27}{125}} = \frac{\sqrt[3]{- 1 \times 27}}{\sqrt[3]{125}} = \frac{\sqrt[3]{(- 1) \times (- 1) \times (- 1) \times 3 \times 3 \times 3}}{\sqrt[3]{5 \times 5 \times 5}} = \frac{\sqrt[3]{(- 1)^{3} \times 3^{3}}}{\sqrt[3]{5^{3}}} = \frac{- 1 \times 3}{5} = \frac{- 3}{5}$

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