Question

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

(i) 2800  (ii) 1620

Answer 1

(i) 2800 can be factorised as follows.

2	2800
2	1400
2	700
2	350
5	175
5	35
7	7
	1

2800 = 2 x 2 x 2 x 2 x 5 x 5 x 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, 2800 has to be divided by 7 to obtain a perfect square.

2800 ÷7 = 400 is a perfect square

400 = 2 x 2 x 2 x2 x 5 x 5

∴ √ 400 = 2 x 2 x 5 = 20

(ii) 1620 can be factorised as follows.

2	1620
2	810
3	405
3	135
3	45
3	15
5	5
	1

1620 = 2 x 2 x 3 x 3 x 3 x 3 x 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, 1620 has to be divided by 5 to obtain a perfect square.

1620 ÷5 = 324 is a perfect square.

324 =  2 x 2 x 3 x 3 x 3 x 3 

∴ √324 = 2 x 3 x 3 = 18