Find the least number that should be added to 9108 to make it a perfect
square. Also, find the square root of the number so obtained.
Answers
Answer:
2 | 9108 {factorization}
2 | 4554
3 | 2277
3 | 759 9108 = |2×2 |×|3×3 |×11×23
11 | 253 = 11×23
23 | 23 = 253
| 1
Thus,253 should be added to 9108 to make it perfect square.
9108+253
=9361
_/9361 = 96.75
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Given : Number 9108
To Find : least number that should be added to 9108 to make it a perfect square
Solution:
95
9108
9 81
_____
1008
185 925
______
83
=> 96 > √9108 > 95
Hence next perfect square is 96²
(96)²
= (100 - 4)²
= 100² + 4² - 2(100)4
= 10000 + 16 - 800
= 9216
9216 - 9108 = 108
Hence 108 must be added to 9108 to make it perfect square
and square root of the number so obtained is 96.
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