On prime factorising, we get, 125=5 × 5× 5 #160; = 5^3 64=2×2×2×2×2×2= 4 × 4× 4 #160; = 4^3 .Then, √(125 × 64)=√(5^3×4^3)= 5×4=20 .Th ...

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Cube Root Using Prime Factorisation

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Question

Evaluate $\sqrt[3]{125 \times 64}$ .

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Solution

On prime factorising, we get,
$125 = 5 \times 5 \times 5$ $= 5^{3}$
$64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 4 \times 4 \times 4$ $= 4^{3}$ .
Then,
$\sqrt[3]{125 \times 64} = \sqrt[3]{5^{3} \times 4^{3}} = 5 \times 4 = 20$ .
Therefore, $20$ is the solution.

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