The correct option is D 8 On prime factorising, we get, 512=2× 2× 2×2× 2× 2×2×2×2 #160; #160; #160; #160; =2^3× 2^3× 2^3=8^3 .Then, ...

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Cube Root Using Prime Factorisation

√-512=?

Question

$\sqrt[3]{- 512} =$ ?

- 64

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- 8

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Not defined

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None of these

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Solution

The correct option is D $- 8$
On prime factorising, we get,
$512 = 2 \times 2 \times 2 - -------- - \times 2 \times 2 \times 2 - -------- - \times 2 \times 2 \times 2 - -------- -$
$= 2^{3} \times 2^{3} \times 2^{3} = 8^{3}$ .
Then, $- 512$ $= (- 8)^{3}$ .
Therefore, cube root of $- 512$ ,
i.e. $\sqrt[3]{- 512} = \sqrt[3]{(- 8)^{3}} = - 8$ .
Therefore, option $B$ is correct.

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