Question

Find the smallest number by which 2592 be multiplied so that the product is a perfect square.

Answer 1

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.