Q. 165.0( 1 Vote )

# Prove that is anirrational number.

Let be a rational number, say r
Then

On squaring both sides,

using (a  +  b) 2 =a 2 +  2ab  +  b 2

Now is a rational number and is an irrational number.
Since a rational number cannot be equal to an irrational number. Our assumption that
is rational is wrong.

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