**Q) **Prove that √5 is an irrational number.

**Ans: **Let us assume that √5 is a rational number

Let √5 = ; where q ≠ 0 and let p, q are co-primes.

5q^{2} = p^{2}………………. (i)

It means p^{2} is divisible by 5

p is divisible by 5

Hence, we can write that p = 5a, where a is an integer……. (ii)

Substituting this value in equation (i), we get:

5q^{2} = (5a)^{2}

5q^{2} = 25a^{2}

q^{2} = 5a^{2}

It means that q^{2} is divisible by 5

q is divisible by 5

Hence, we can write that q = 5b, where b is an integer…… (iii)

From equation (ii) and (iii), we get that p and q are not co-primes, which contradicts to our initial assumption.

**Therefore, √5 is an irrational number****………… Hence Proved !**