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Question
The least number by which 125 be multiplied to make it a perfect square is ______.
Solution
The least number by which 125 be multiplied to make it a perfect square is 5.
Explanation:
| 5 | 125 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Resolving 125 into prime factors, we get
125 = 5 × 5 × 5
Grouping the factors in triplets of equal factors, we get
125 = (5 × 5) × 5
We observe that 5 is without a pair.
Thus, we must multiply the number by 5, so that the product is a perfect square.
Hence, the least number, which should be multiplied with 125 to make it a perfect square, is 5.
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