Prove that following numbers are irrational:

Let be a rational number.

Therefore,, where g. c. d(a, b) = 1 and a, b N.

Now, squaring both sides

……. eq (1)

5 | a²

5 | a

Now, let a = 5k, k N

So, b = 5k

5 | b

It is a contradiction as g. c. d (a, b) = 1

So, our assumption is wrong.

Therefore, is irrational.