Prove that following numbers are not rational :

5√3

Let us assume that 5 be a rational number.

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

Now, =5

=

Since, a is an integer and 3b is also an integer (5b ≠ 0)

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, 5 is an irrational number.