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.
400
Find the square root of the following number by the prime factorisation method.
9216
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.
180
Find the smallest number by which the given number must bew multiplied so that the product is a perfect square:
23805
Write true (T) or false (F) for the following statement.
The number of digits in a square number is even.
Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
25
Find the square rootthe following by prime factorization.
11664
Find the least square number, exactly divisible by each one of the number:
8, 12, 15 and 20
Find the square root by prime factorisation method
9025
A square board has an area of 144 square units. How long is each side of the board?
