Prove that is irrational.

Let us assume that be a rational number.

Then, it will be of the form where a and b are co-prime and b≠0.

Now, =

=

=

Since, 5a is an integer and b is also an integer

So, is a rational number

is a rational number

But this contradicts to the fact that is an irrational number.

Therefore, our assumption is wrong.

Hence, is an irrational number.