Question

Q29 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 cube.

Answer 1

No 392 is not a perfect cube.

Answer 2

Step-by-step explanation:

$Resolving \: 392 \: into \: prime \: factors, \\we \:get$

2 | 392

_______

2 | 196

_______

2 | 98

_______

7 | 49

_______

**** 7

392 = 2 × 2 × 2 × 7 × 7

The Prime factor 7 doesn't appear in a group of three factors.

So, 392 is not a perfect cube .

Hence, the smallest number by which it is be multiplied to make it a perfect cube is 7.

Now,

392 × 7 = 2 × 2 × 2 × 7 × 7 × 7

$= 2^{3} \times 7^{3}\\= (2\times 7)^{3}\\=14^{3}$

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