Prime Factorisation of 632:
To determine if 632 is a perfect square, we need to find the prime factorisation of 632.

The prime factorisation of a number is the expression of that number as a product of its prime factors. To find the prime factorisation of 632, we can use the following steps:

1. Divide the number by the smallest prime number, which is 2, and continue dividing until we can no longer divide evenly.
- 632 ÷ 2 = 316
- 316 ÷ 2 = 158
- 158 ÷ 2 = 79

2. The last quotient, 79, is a prime number.

Therefore, the prime factorisation of 632 is: 2 × 2 × 2 × 79, or in exponent form: 2^3 × 79.

Perfect Square Test:
To determine if 632 is a perfect square, we need to examine the exponents of its prime factors. If all the exponents are even, then the number is a perfect square.

In the prime factorisation of 632, we have 2^3 × 79.

- The exponent of 2 is 3, which is odd.
- The exponent of 79 is 1, which is also odd.

Since the exponents are not all even, we can conclude that 632 is not a perfect square.

Conclusion:
Using prime factorisation, we determined that the prime factorisation of 632 is 2^3 × 79. By examining the exponents of its prime factors, we found that the exponents are not all even. Therefore, 632 is not a perfect square.