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Explain why a number of the form 4q+2, can never a perfect square

Posted by Suresh Gupta 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 4 months ago

No number of the form 4q + 2 is a perfect square because,
If q is a prime factor of a
perfect square, then q^2 must also be the factor of a perfect square.
4q + 2 = 2 (2q + 2), here 2 is a factor of (2q + 2), but 2^2 = 4 is not the factor of (4q + 2) as (4q + 2) = 2(2q + 1), which is odd and we know that all the odd numbers are not divisible by 2.

So, we can say that 4q + 2 is not divisible by 4
Hence, 4q + 2 is not a perfect

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CBSE > Class 10 > Mathematics