There are essentially two ways that I know to solve this.
One is to guess.
The other is to find the prime factors of 96. For an integer to be a perfect square, each prime factor has to occur an even number of time. Therefore k would need to be the product of whatever primes occur in 96 an odd number of times.
Given that 9+6 is divisible by 3, we know that 96 is divisible by 3. Doing the division, we find that 96 = 3 * 32.
The prime factor 3 only occurs once. Therefore k must be a multiple of 3.
32 is 2 raised to the 5th power. This is an odd number of 2’s. We need one more. Therefore k must be a multiple of 2.
Therefore the smaller possible value of k is 6.
96 * 6 is a perfect square. It is the same as 64 * 9, or 24 * 24.
Hope it helps!
