(i)252 can be factorised as follows.
2 |
252 |
2 |
126 |
3 |
63 |
3 |
21 |
7 |
7 |
|
1 |
252 = 2 × 2 × 3 × 3 × 7
Here, prime factor 7 does not have its pair. If 7 gets a pair, then the number will become a perfect square. Therefore, 252 has to be multiplied with 7 to obtain a perfect square.
252 × 7 = 2 × 2 × 3 × 3 × 7 × 7
Therefore, 252 × 7 = 1764 is a perfect square
∴ √1764 = 2 x 3 x 7 = 42
(ii)180 can be factorised as follows.
2 |
180 |
2 |
90 |
3 |
45 |
3 |
45 |
5 |
5 |
|
1 |
180 = 2 × 2 × 3 × 3 × 5
Here, prime factor 5 does not have its pair. If 5 gets a pair, then the number will become a perfect square. Therefore, 180 has to be multiplied with 5 to obtain a perfect square.
180 × 5 = 900 = 2 × 2 × 3 × 3 × 5 × 5
Therefore, 180 × 5 = 900 is a perfect square.
∴ √900 = 2 x 3 x 5 = 30