Square and Square Roots Class 8
Exercise
1. Using prime factorization method, find which of the following are perfect square numbers :
2 | 126
3 | 63
3 | 21
7 | 7
| 1
252 = 2 *2 * 3 * 3 * 7
Thus, 252 cannot be expressed as the product of pairs of equal factors,
Hence , 252 is not a perfect square.
ii) 324
: 2 | 324 2 | 162 3 | 81
3 | 27
3 | 9
3 | 3
| 1
324 = 2 *2 * 3 * 3 * 3 * 3
Thus, 324 can be expressed as the product of pairs of equal factors,
Hence , 324 is a perfect square.
- iii) 5625 :
5 | 5625
5 | 1125
5 | 225
5 | 45
3 | 9
3 | 3
| 1
5625 = 5 * 5 * 5 * 5 * 3 * 3
Thus, 5625 can be expressed as the product of pairs of equal factors,
Hence , 5625 is a perfect square.
5 | 9075
5 | 1815
3 | 363
11 | 121
11 | 11
| 1
9075 = 5 * 5 * 11 * 11 * 3
Thus, 9075 cannot be expressed as the product of pairs of equal factors,
Hence , 9075 is not a perfect square.
2. Show that each of the following numbers is a perfect square. Also, find the square root of each.
5 | 1225
5 | 245
7 | 49
7 | 7
| 1
1225 = 5 * 5 * 7 * 7
It is perfect square.
√1225 = 5 * 7 = 35
- 3969:
3 | 3969
3 | 1323
3 | 441
3 | 147
7 | 49
7 | 7
| 1
3969 = 3 * 3 * 3 * 3 * 7 * 7
It is perfect square.
√3969 = 3 * 3 * 7 = 63
- 8281
7 | 8281 7 | 1183
13 | 169
13 | 13
| 1
|
8281 = 7 * 7 * 13 *13
It is perfect square.
√8281 = 7 * 7 * 13 * 13 = 91
3. Find the smallest number by which each of the following number must be multiplied to get a perfect square number. Also, find the square root of the resulting number.
2 | 3332
2 | 1666
7 | 833
7 | 119
17 | 17
| 1
3332 = 2 *2 * 7 * 7 * 17
Thus, 2 and 7 exist in pairs while 17 is alone.
So, we should multiply the given number by 17 to get perfect square number.
Perfect square number so obtained = 3332 * 17 = 56644
56644 = 2 * 2 * 7 * 7 * 17 * 17
√56644 = 2 * 7 * 17 = 238
2 | 2592
2 | 1296
2 | 648
2 | 324
2 | 162
3 | 81
3 | 27
3 | 9
3 | 3
| 1
2592 = 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3 * 3
Thus, 2 , 2 , 3, 3 exist in pairs while 2 is alone.
So, we should multiply the given number by 2 to get perfect square number.
Perfect square number so obtained = 2592 * 2 = 5184
5184 = 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3 * 3
√5184 = 2 * 2 * 2 * 3 * 3 = 72
4. By which least number should be a given number be divided to get a perfect square number. Also, find the square root of the resulting number.
2 | 1728
2 | 864
2 | 432
2 | 216
2 | 108
2 | 54
3 | 27
3 | 9
3 | 3
| 1
1728 = 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3
There are 4 pair of equal factors. 3 do not exists in pair.
So, we must divide the given number by 3
i) Perfect square number obtained = 1728 / 3 = 576
ii) √ 576 = 24
2 | 8820
2 | 4410
3 | 2205
3 | 735
5 | 245
7 | 49
7 | 7
| 1
1728 = 2 * 2 * 3 * 3 * 7 * 7 * 5
There are 3 pair of equal factors.5 do not exists in pair.
So, we must divide the given number by 5
i) Perfect square number obtained = 8820 / 5 = 1764
ii) √ 1764 = 42
Post a Comment