(i) 1008 can be factorised as follows.
2 |
1008 |
2 |
504 |
2 |
252 |
2 |
126 |
3 |
63 |
3 |
21 |
7 |
7 |
|
1 |
1008 = 2 × 2 × 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, 1008 can be multiplied with 7 to obtain a perfect square.
1008 × 7 = 7056 = 2 × 2 ×2 × 2 × 3 × 3 × 7 × 7
Therefore, 1008 × 7 = 7056 is a perfect square.
∴ √7056 = 2 x 2 x 3 x 7 = 84
(ii) 2028 can be factorised as follows.
2 |
2028 |
2 |
1014 |
3 |
507 |
13 |
169 |
13 |
13 |
|
1 |
2028 = 2 × 2 × 3 × 13 × 13
Here, prime factor 3 does not have its pair. If 3 gets a pair, then the number will become a perfect square. Therefore, 2028 has to be multiplied with 3 to obtain a perfect square.
Therefore, 2028 × 3 = 6084 is a perfect square.
2028 × 3 = 6084 = 2 × 2 × 3 × 3 × 13 × 13
∴ √6084 = 2 x 3 x 13 = 78