For each of the following number find the smallest whole number by which it should be divided so as to get perfect square also also find the square root of the square numbers obtained .
1) 2925
2) 2800
3)2645
Answers
252 can be factorised as follows.
2
252
2
126
3
63
3
21
7
7
1
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.
252 ÷7 = 36 is a perfect square.
(ii) 2925 can be factorised as follows.
3
2925
3
975
5
325
5
65
13
13
1
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.
2925 ÷13 = 225 is a perfect square.
(iii)396 can be factorised as follows.
2
396
2
198
3
99
3
33
11
11
1
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.
396 ÷11 = 36 is a perfect square.
(iv) 2645 can be factorised as follows.
5
2645
23
529
23
23
1
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.
2645 ÷5 = 529 is a perfect square.
(v)2800 can be factorised as follows.
2
2800
2
1400
2
700
2
350
5
175
5
35
7
7
1
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.
2800 ÷7 = 400 is a perfect square.
∴
(vi)1620 can be factorised as follows.
2
1620
2
810
3
405
3
135
3
45
3
15
5
5
1
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, 1620 has to be divided by 5 to obtain a perfect square.
1620 ÷5 = 324 is a perfect square