The correct option is C 0.2 We know, 0.008 = 8 × 10 ^ 3 =8 ×110×110×110 .Also, on prime factorising 8 , we get, 8=2× 2× 2=2^3 .Then, √( ...

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Cube Root Using Prime Factorisation

Value of √0...

Question

Value of $\sqrt[3]{0.008}$ is:

0.2

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0.4

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0.002

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None

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Solution

The correct option is C $0.2$
We know,
$0.008 = 8 \times 10^{- 3} = 8 \times \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10}$ .

Also, on prime factorising $8$ , we get,
$8 = 2 \times 2 \times 2 = 2^{3}$ .

Then, $\sqrt[3]{0.008}$ $= \sqrt[3]{8 \times \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10}}$
$= \sqrt[3]{2^{3} \times \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10}}$
$= 2 \times \frac{1}{10} = 0.2$ .

Hence, option $A$ is correct.

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