Question

1. Is 176 a perfect square? if not find the smallest number by which it should be multiplied to get a perfect square.

Answer 1

$\mathbb{ SOLUTION }$ :

Prime factors of 176 = 2 × 2 × 2 × 2 × 11

so, 176 = 2² × 2² × 11

Here, 11 has no pair.

So, it is not a perfect square and 11 is the smallest number by which 176 should be multiplied to get a perfect square.

Then,

176 × 11 = 2² × 2² × 11 × 11

1936 = 2² × 2² × 11²

1936 = (44)²

$\therefore$ Hence, the smallest number is 11 by which 176 should be multiplied to get a perfect square.

Answer 2

no it not perfect square
by multiple 11 it became 1936
√1936=44