# Q.6 For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained.(i) 252(ii) 2925(iii) 396(iv) 2645(v) 2800(vi) 1620

(i) 252: Prime factorization of 252 gives = .

For making pairs we will divide the given number by 7.

The obtained number is 36 and its square root is 6.

(ii) 2925: Prime factorization of 2925 gives =

To make pairs divide the given number by 13.

So the obtained number is 225 and its square root is 15.

(iii) 396: Prime factorization if 396 =

For obtaining perfect square number we need to divide the given number by 11.

So the required number is 36 and its square root is 6.

(iv) 2645: Prime factorization of 2645 =

We need to divide the given number by 5 to obtain the perfect square number.

So the obtained number is 529 and its square root is 23.

(v) 2800:      Prime factorization of 2800  =

To make pairs we need to divide 2800 by 7.

So the required number is 400 and its square root is 20.

(vi) 1620: Prime factorization of 1620 gives =

To make pairs divide the given number by 5.

We get , number = 324 and its square root = 18.

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