For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square

(i) 252 can be factorized as follows:

252 = 2 * 2 * 3 * 3 * 7 

Here, prime factor 7 doesnot have its pair

If we divide this number by 7, the n the number will be come a perfect square.

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

252/7 =36 is a perfect square

36 = 2 * 2 * 3 * 3

√36 = 2 * 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 be come a perfect square.

There fore, 2925 has to be divided by 13 to obtain aperfect square

2925/13 = 225 is a perfect square

225 = 3 * 3 * 5 * 5

√225 =  3 * 5

=15

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

396 = 2 * 2 * 3 * 3 * 11

Here, primefactor 11 doesnot have its pair

If we divide this number by 11, then the numbe rwill be come aperfect square.

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

isaperfectsquare

36=2 * 2 * 3 * 3

√36 = 2 * 3

=6

(iv)The prim efact or ization of 2645 is as follows:

2645 = 5* 23 * 23

Here, prim efact or 5 does not have its pair

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

2645/5 = 529 is a perfect square

529 = 23 * 23

√529 = 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 be come a perfect square. There fore , 2800 has to be divided by 7 to obtain a perfect square

2800/7 = 400 is a perfect square

400 = 2 * 2 * 2 * 2 * 5 * 5

√400 = 2 * 2 *5

= 20

(vi)  The prim efactorization of 1620 is as follows:

1680 = 2* 2 * 3 * 3 * 3 * 3 * 5

Here, primefactor 5 doesnot have its pair

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

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

1620/5 = 324 is a perfect square

324 = 2 * 2 * 3 * 3 * 3 * 3

√324 = 2 * 3 * 3

=18