# Prove that is an irrational number.

If possible, let be a rational number equal to x. Then,

x = x2 = ( )2

= ( )2 + ( )2 + 2 * * = 3 + 5 + 2 = 8 + 2 x2 – 8 = 2  = Now, x is rational

x2 is rational is rational is rational

But, is irrational

Thus, we arrive at a contradiction. So, our supposition that + is rational is wrong.

Hence, + is an irrational number.

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