Question

. Is 392 a perfect cube? If not find the smallest natural number by which 392 must be multiplied so that
the product is a perfect​

Answer 1

no, it is not a perfect cube because the factors of 392 are= 2*2*2*7*7 we want one more 7 to make it a perfect cube.

$3 \sqrt{3} 92$

=

$\sqrt{2 \times 2 \times 2 \times 7 \times 7}$

multiply 7 by both sides

$\sqrt{392 \times 7} =$

$\sqrt{2 \times 2 \times 2 \times 7 \times 7 \times 7}$

then,

$\sqrt{2734 = }$

2*7= 14 ans

Answer 2

Step-by-step explanation:

$392 = 2 \times 2 \times 2 \times7 \times 7$

The Prime factor 7 does not appear in a group of three. Therefore, 392 is not a perfect cube. To make it's a cube, we need one more 7. In that case

$\tiny{392 \times 7 = 2 \times 2 \times 2 \times 7 \times 7 \times 7 = 2744}$

Hence the smallest natural number by which 392 should be multiplied to make a perfect cube is 7.