**Solution: **

Let us assume, that **√**5 is a rational number.

i.e. **√**5 = x/y (where, x and y are co-primes)

y**√**5= x

Squaring on both sides, we get,

(y**√**5)^{2} = x^{2}

⇒ 5y^{2} = x^{2}…. (1)

Thus, x^{2} is divisible by 5, so x is also divisible by 5.

Let us say, x = 5k, for some value of k and substituting the value of x in equation (1), we get,

5y^{2} = (5k)^{2}

⇒ y^{2} = 5k^{2}

is divisible by 5 it means y is divisible by 5.

Clearly, x and y are not co-primes. Thus, our assumption about **√**5 is rational is incorrect.

Hence, **√**5 is an irrational number.