Ans:  Let √5 be a rational number.  

Therefore √5 = p/q, where q ≠ 0 and let p & q be co-primes. 

⇒ 5q² = p² 

⇒ p² is divisible by 5 

⇒ p is divisible by 5………………….. ……………….. (i) 

⇒ p = 5a, where a is some integer  

25a² = 5q² 

⇒ q² = 5a² 

⇒ q² is divisible by 5 

⇒ q is divisible by 5………………………………………..(ii) 

⇒ q = 5b, where b is some integer

(i) and (ii)  leads to contradiction as ‘p’ and ‘q’ are co-primes. 

Therefore, √5 is an irrational number.