On prime factorisation of the numbers individually, we get, 8= 2 × 2 × 2 =2^3 . 125= 5 × 5 × 5 =5^3 .Therefore, √( 8 × 125 ) = √(2^3 × 5^3)=2 × 5=10 ...

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Standard VIII

Mathematics

Cube Roots

Evaluate: √...

Question

Evaluate: $\sqrt[3]{8 \times 125}$ .

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Solution

On prime factorisation of the numbers individually, we get,
$8 = 2 \times 2 \times 2 - -------- - = 2^{3}$ .

$125 = 5 \times 5 \times 5 - -------- - = 5^{3}$ .

Therefore,
$\sqrt[3]{8 \times 125} = \sqrt[3]{2^{3} \times 5^{3}} = 2 \times 5 = 10$ .

Thus, $10$ is the solution.

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Evaluate: 3√8×125.

On prime factorisation of the numbers individually, we get,8=2×2×2––––––––––=23.125=5×5×5––––––––––=53.Therefore,3√8×125=3√23×53=2×5=10.Thus, 10 is the solution.

Evaluate: $\sqrt[3]{8 \times 125}$ .

On prime factorisation of the numbers individually, we get,
$8 = 2 \times 2 \times 2 - -------- - = 2^{3}$ .

$125 = 5 \times 5 \times 5 - -------- - = 5^{3}$ .

Therefore,
$\sqrt[3]{8 \times 125} = \sqrt[3]{2^{3} \times 5^{3}} = 2 \times 5 = 10$ .

Thus, $10$ is the solution.