Question

Is 2,925 a perfect square? If yes, find its square root. If no, find the smallest number which should be multiplied
so that the resulting number is a perfect square.​

Answer 1

SoluTion :-

Given number = 2925

Resolving 2925 into prime factors, we get :

2925 = 3 × 3 × 5 × 5 × 13

Clearly, 2925 cannot be expressed as a product of pairs of equal factors.

Thus, it is not a perfect square.

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2925 = 3 × 3 × 5 × 5 × 13

We can see that 3 and 5 exist in pairs while 13 is alone.

So, we should multiply the given number by 13 to get a perfect square number.

(i) Perfect square number so obtained = 2925 × 13 = 38025

(ii) Now, 38025 = 3 × 3 × 5 × 5 × 13 × 13