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Can any body explain this DS in a more detailed manner please? Thank you.
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Can any body explain this DS in a more detailed manner please? Thank you.

If x and y are positive integers, is \(\sqrt{2xy}\) an integer?

(1) y – x = 0. Rearrange to get x = y.

Hence, \(\sqrt{2xy}=\sqrt{2x^2}=x\sqrt{2}=integer*irrational\neq integer\) (x is an integer and \(\sqrt{2}\) is an irrational number. The product of a non-zero integer and an irrational number cannot be an integer). Sufficient.

(2) xy = 1.

Hence, \(\sqrt{2xy}=\sqrt{2}=irrational\neq integer\). Sufficient.

Answer: D.

Hope it's clear.
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