The correct option is D 56√(392)×√(448) =√(2 × 2 × 2 × 7 × 7)×√(2 × 2 × 2× 2 × 2 × 2 × 7) =√((2 × 2 × 2)× (2 × 2 × 2)× (2 × 2 × 2) × (7 × 7 × 7)) = 2 × 2 × 2 × ...

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Cube Root Using Prime Factorisation

Value of √392...

Question

Value of $\sqrt[3]{392} \times \sqrt[3]{448}$ is ______.

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Solution

The correct option is D 56
$\sqrt[3]{392} \times \sqrt[3]{448}$
$= \sqrt[3]{2 \times 2 \times 2 \times 7 \times 7} \times \sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7}$
$= \sqrt[3]{(2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (7 \times 7 \times 7)}$
$= 2 \times 2 \times 2 \times 7$
$[∵ \sqrt[3]{p} \times \sqrt[3]{q} = \sqrt[3]{p q}]$
$= 56$

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Value of $\sqrt[3]{392} \times \sqrt[3]{448}$ is

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Value of 3√392×3√448 is ______.

The correct option is D 563√392×3√448 =3√2×2×2×7×7×3√2×2×2×2×2×2×7 =3√(2×2×2)×(2×2×2)×(2×2×2)×(7×7×7) =2×2×2×7 [∵3√p×3√q=3√pq] =56

Value of $\sqrt[3]{392} \times \sqrt[3]{448}$ is ______.