√ n is always a rational number only if n is a ___________________
vidya854:
if n is a perfect square
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square root of any number
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Since n is an integer, so is (ab)2(ab)2. There are two possibilities:
1) abab is an irrational number which is not possible.
2) abab is a rational number. Therefore it is an integer because (ab)2(ab)2 is. Since abab is an integer, there is some q∈Zq∈Z such that a=b.qa=b.q. Hence n=q2n=q2.
1) abab is an irrational number which is not possible.
2) abab is a rational number. Therefore it is an integer because (ab)2(ab)2 is. Since abab is an integer, there is some q∈Zq∈Z such that a=b.qa=b.q. Hence n=q2n=q2.
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