Advertisements
Advertisements
Question
Find the smallest number by which 2592 be multiplied so that the product is a perfect square.
Advertisements
Solution
2592 = `bar(2xx2) xx bar(2xx2) xx 2 xx bar(3xx3) xx bar(3xx3)`
On grouping the prime factors of 2592 as shown; on factor i.e. 2 is left which cannot be paired with equal factor.
| 2 | 2592 |
| 2 | 1296 |
| 2 | 648 |
| 2 | 324 |
| 2 | 162 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
2 is the smallest number that must be multiplied by 2592 to get a perfect square.
2592 × 2 = 5184.
The prime factorization of 5184 is:
5184 = 26.34
Both powers (6 and 4) are even, so 5184 is a perfect square.
The smallest number is 2.
APPEARS IN
RELATED QUESTIONS
Find the square root of the following number by the prime factorisation method.
9604
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.
1458
Find the smallest number by which the given number must bew multiplied so that the product is a perfect square:
7688
Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
25
Find the smallest number by which 12748 be mutliplied so that the product is a perfect square?
Find the square root by prime factorisation method
256
Find the square root by prime factorisation method
1156
Using prime factorisation, find which of the following are perfect squares.
729
