(i) 1458 can be factorised as follows.
2 |
1458 |
3 |
729 |
3 |
243 |
3 |
81 |
3 |
27 |
3 |
9 |
3 |
3 |
|
1 |
1458 = 2 × 3 × 3 × 3 × 3 × 3 × 3
Here, prime factor 2 does not have its pair. If 2 gets a pair, then the number will become a perfect square. Therefore, 1458 has to be multiplied with 2 to obtain a perfect square.
Therefore, 1458 × 2 = 2916 is a perfect square.
1458 × 2 = 2916 = 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3
∴ √2916 = 2 x 3 x 3 x 3 = 54
(ii) 768 can be factorised as follows.
2 |
768 |
2 |
384 |
2 |
192 |
2 |
96 |
2 |
48 |
2 |
24 |
2 |
12 |
2 |
6 |
3 |
3 |
|
1 |
768 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
Here, prime factor 3 does not have its pair. If 3 gets a pair, then the number will become a perfect square. Therefore, 768 has to be multiplied with 3 to obtain a perfect square.
Therefore, 768 × 3 = 2304 is a perfect square.
768 × 3 = 2304 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
∴ √2304 = 2 x 2 x 2 x 2 x 3 = 48