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# Explain why 3^3 x 2^2 is not a perfect square?? watch

1. Maths gcse question. I don't how to explain this.
(Without calculation)
2. the prime factor list of a perfect square must have an even number of factors....

3*3*3*3*3*3*2*2*2*2*2*2*2*2*2*2 must be a perfect square but

3*3*3*3*3*3*2*2*2*2*2*2*2*2*2 is not

3*3*3*3*3*2*2*2*2*2*2*2*2*2*2 is not
3. (Original post by Sizzo1128)
Maths gcse question. I don't how to explain this.
(Without calculation)
which clearly isn't of the form for any +ve integer
4. Essentially for a number to be a perfect square you need to be able to split its prime factorisation into two equal lists. For example:

is a perfect square because you can split into into two lists comprised of
is not a perfect square because you cannot separate multiplications.

The general rule is that if a prime factor is raised to an odd power, it is not a perfect square

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Updated: November 7, 2017
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