I have a theory that i need to prove but im not quite sure how to mathematically prove that it is true.(adsbygoogle = window.adsbygoogle || []).push({});

Theory: When you square a rational number, each of the prime factors has an even exponent.

For example,

10 --> If i square 10, which is a rational number,

=10^2

=(5^2 x 2^2) --> both 5 and 2 are prime, and have even exponents. Thus, 10 is a rational number.

√7 ?

=(√7)^2

=7^1 --> odd exponent, thus irrational number.

I want to prove this will work for any case. Any ideas??

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# Prove that a rational number squared has each of its prime factors with even exponent

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