√( 512) nbsp;= √( 1 × 512) = √(( 1)× ( 1)×( 1)×2 × 2 × 2×2 × 2 × 2×2 × 2 × 2) = √(( 1)^3 × (2)^3 × (2)^3 × (2)^3)= 1 × 2 × 2× 2 = 8Therefore, √( 512)= 8. ...

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Byju's Answer

Standard VIII

Mathematics

Cube Root Using Prime Factorisation

Evaluate: √-5...

Question

Evaluate:
$\sqrt[3]{- 512}$

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Solution

$\sqrt[3]{- 512}$
$=$ $\sqrt[3]{- 1 \times 512}$
$=$ $\sqrt[3]{¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ (- 1) \times (- 1) \times (- 1) \times ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 2 \times 2 \times 2 \times ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 2 \times 2 \times 2 \times ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 2 \times 2 \times 2}$
$=$ $\sqrt[3]{(- 1)^{3} \times (2)^{3} \times (2)^{3} \times (2)^{3}}$
$=$ $- 1 \times 2 \times 2 \times 2 = - 8$
Therefore, $\sqrt[3]{- 512} = - 8$ .

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Evaluate: 3√−512

Evaluate:
$\sqrt[3]{- 512}$