For each of the following numbers, find the smallest whole number by which it shouldbe divided so as to get a perfect square. Also find the square root of the squarenumber so obtained.

(i) 252 (ii) 2925

(iii) 396 (iv) 2645

(v) 2800 (vi) 1620

(i) 252 can be factorized as follows:

252 = __2 * 2__ * __3 * 3__ * 7

Here, prime factor 7 does not have its pair

If we divide this number by 7, then the number will become a perfect square.

Therefore, 252 has to be divided by 7 to obtain a perfect square

is a perfect square

36 = __2 * 2__ * __3 * 3__

= 6

(ii) The prime factorization of 2925 is as follows:

2925 = __3 * 3__ * __5 * 5__ * 13

Here, prime factor 13 does not have its pair

If we divide this number by 13, then the number will become a perfect square.

Therefore, 2925 has to be divided by 13 to obtain a perfect square

is a perfect square

225 = __3 * 3__ * __5 * 5__

= 15

(iii) The prime factorization of 396 is as follows:

396 = 2 * 2 * 3 * 3 * 11

Here, prime factor 11 does not have its pair

If we divide this number by 11, then the number will become a perfect square.

Therefore, 396 has to be divided by 11 to obtain a perfect square

is a perfect square

36 = __2 * 2__ * __3 * 3__

= 6

(iv) The prime factorization of 2645 is as follows:

2645 = 5 * __23 * 23__

Here, prime factor 5 does not have its pair

If we divide this number by 5, then the number will become a perfect square. Therefore, 2645 has to be divided by 5 to obtain a perfect square

is a perfect square

529 = __23 * 23__

= 23

(v) 2800 can be factorized as follows:

2800 = __2 * 2__ * 7 * __10 * 10__

Here, prime factor 7 does not have its pair

If we divide this number by 7, then the number will become a perfect square. Therefore, 2800 has to be divided by 7 to obtain a perfect square

is a perfect square

400 = __2 * 2__ * __2 * 2__ * __5 * 5__

= 2 * 2 * 5

= 20

(vi) The prime factorization of 1620 is as follows:

1680 = __2 * 2__ * __3 * 3__ * __3 * 3__ * 5

Here, prime factor 5 does not have its pair

If we divide this number by 5, then the number will become a perfect square.

Therefore, 1680 has to be divided by 5 to obtain a perfect square

is a perfect square

324 = __2 * 2__ * __3 * 3__ * __3 * 3__

= 18

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