Question

Find the cube root of the product of the numbers 343 and 512

Answer 1

343×512=175616
3√175616 =56

Answer 2

Answer:

$\sqrt[3]{343\times 512}=56$

Step-by-step explanation:

Resolving 343 and 512 into Prime factors , we get

343 = 7×7×7

and

512 = 8×8×8

Now ,

343 × 512 = (7×7×7)×(3×3×3)

$\sqrt[3]{(343\times 512)}\\=\sqrt[3]{(7\times 7 \times 7)\times (8\times 8 \times 8)}\\=7\times 8\\=56$

Therefore,

$\sqrt[3]{343\times 512}=56$

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