Question

For the following number, 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.

2800

Answer 1

2800 can be factorised as follows.

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

2800 = 2 × 2 × 2 × 2 × 5 × 5 × 7

Here, prime factor 7 does not have its pair.

If we divide this number by 7, 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 × 2 × 2 × 2 × 5 × 5

∴ `sqrt400` =  2 ×  2 × 5 = 20