Advertisements
Advertisements
Question
The least number by which 125 be multiplied to make it a perfect square is ______.
Advertisements
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.
APPEARS IN
RELATED QUESTIONS
Find the square root of the following number by the prime factorisation method.
5929
Find the square root of the following number by the prime factorisation method.
529
For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.
768
Find the smallest square number that is divisible by each of the numbers 4, 9, and 10.
Write true (T) or false (F) for the following statement.
There are fourteen square number upto 200.
Find the square rootthe following by prime factorization.
11664
Find the smallest number by which 147 must be multiplied so that it becomes a perfect square. Also, find the square root of the number so obtained.
By splitting into prime factors, find the square root of 194481.
Examine if the following is a perfect square
725
Is 176 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.
