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

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    Maths gcse question. I don't how to explain this.
    (Without calculation)
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    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
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    (Original post by Sizzo1128)
    Maths gcse question. I don't how to explain this.
    (Without calculation)
    3^3 \cdot 2^2 = 3\cdot (3\cdot 2)^2 which clearly isn't of the form a^2 for any +ve integer a
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    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:

     5^2 \times 7^4 is a perfect square because you can split into into two lists comprised of  5, 7
     7^3 \times 2^2 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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