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.
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) 252 (ii) 2925
3 Answers
(i) 252 can be factorised as follows.
| 2 | 252 |
| 2 | 126 |
| 3 | 63 |
| 3 | 21 |
| 7 | 7 |
| 1 |
252 = 2 x 2 x 3 x 3 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, 252 has to be divided by 7 to obtain a perfect square.
252 ÷7 = 36 is a perfect square.
36 = 2 x 2 x 3 x 3
∴ √36 = 2 x 3 = 6
(ii) 2925 can be factorised as follows.
| 3 | 2925 |
| 3 | 975 |
| 5 | 325 |
| 5 | 65 |
| 13 | 13 |
| 1 |
2925 = 3 x 3 x 5 x 5 x 13
Here, prime factor 13 does not have its pair. If we divide this number by 13, then the number will become a perfect square. Therefore, 2925 has to be divided by 13 to obtain a perfect square.
2925 ÷13 = 225 is a perfect square.
225 = 3 x 3 x 5 x 5
∴ √225 = 3 x 5 = 15
(i) 396 can be factorised as follows.
| 2 | 396 |
| 2 | 198 |
| 3 | 99 |
| 3 | 33 |
| 11 | 11 |
| 1 |
396 = 2 x 2 x 3 x 3 x 11
Here, prime factor 11 does not have its pair. If we divide this number by 11, then the number will become a perfect square. Therefore, 396 has to be divided by 11 to obtain a perfect square.
396 ÷11 = 36 is a perfect square.
36 = 2 x 2 x 3 x 3
∴ √36 = 2 x 3 = 6
(ii) 2645 can be factorised as follows.
| 5 | 2645 |
| 23 | 529 |
| 23 | 23 |
| 1 |
2645 = 5 x 23 x 23
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, 2645 has to be divided by 5 to obtain a perfect square.
2645 ÷5 = 529 is a perfect square
529 = 23 x 23
∴ √529 = 23
(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