Question

PROVE THAT NO NUMBER OF THE TYPE 4K+2 CAN BE A PERFECT SQUARE

Answer 1

Lemma:
If p is a prime factor of a perfect square, p^2 must also
be a factor of that perfect square.

'
4k+2 = 2(2k+1)
'
2 is a factor of 4k+2 but 2k+1 is odd and cannot have factor 2, so 4k+2 is not divisible by 4, and therefore cannot be a perfect square.

Answer 2

Since:

4k+2 = 100

4k =100 - 2

K= 24.5

4k + 2 = 1

4 k = 1-2

4k = -1

k = -1/4

K = -0.25

Hence , no number of type 4k+2can be a perfect sq.