Question

is 2352 a perfect square if not find the smallest multiple of 2352 which is a perfect square find the square root of the new number

Answer 1

no the smallest multiple is 45

Answer 2

Solution

We have 2352 =2×2×2×2×3×7×7

As the prime factor 3 has no pair, 2352 is not a perfect square.

If 3 get's a pair then the number will become perfect square. So, we multiply 2352 by 3 to get

$2352 \times 3 = 2 \times 2 \times 2 \times 2 \times 3 \times 7 \times 7$

Now, each prime factor is in a pair.Therfore,2352 × =7056 is a perfect square.

Thus the required square smallest multiple is 7056 which is a perfect square.

And

$\sqrt{7056 = 2 \times 2 \times 3 \times 7 = 84}$