Question

find the cube root of 392 × cube root of 448 *full explanation only

Answer 1

This is the answer of ur question

Answer 2

Cube : The cube of a number is the number when exponent is 3.

Perfect cube : A natural number 'n' is said to be a perfect cube if there is an integer 'm' such that

n = m*m*m

$\sqrt[3]{392} \times \sqrt [3]{448} = \sqrt [3]{392 \times 448}\\ Now,\ resolving\ 392\ and\ 448\ into\ prime\ factors,\ we\ get\\ 392 = 2\times2\times2\times7\times7\ and\ 448 = 2\times2\times2\times2\times2\times2\times7\\ \therefore 392 \times 448 = 2\times2\times2\times7\times7\times2\times2\times2\times2\times2\times2\times7$$=\big( 2\times2\times2\times\big)\times \big(2\times2\times2 \big)\times \big(2\times2\times2 \big) \big(7\times7\times7 \big)\\ [tex]\\ \therefore \sqrt [3]{392 \times 448} = 2\times2\times2\times7 = 56 \\ Hence,\ \sqrt[3]{392} \times \sqrt[3]{448} = \sqrt[3]{392 \times 448} = 56$