√( 216) = √(( 1)(216)) = √(( 1)× ( 1)×( 1)×2 × 2 × 2×3 × 3 × 3) = √(( 1)^3 × 2^3 × 3^3) = 1 × 2 × 3 = 6 ...

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Cube Root Using Prime Factorisation

Evaluate : √-...

Question

Evaluate :
$\sqrt[3]{- 216}$

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Solution

$\sqrt[3]{- 216}$ = $\sqrt[3]{(- 1) (216)}$
= $\sqrt[3]{(- 1) \times (- 1) \times (- 1) \times ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 2 \times 2 \times 2 \times ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 3 \times 3 \times 3}$
= $\sqrt[3]{(- 1)^{3} \times 2^{3} \times 3^{3}}$
= $- 1 \times 2 \times 3 = - 6$

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