# 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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