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.