Question

√2 is 

(a) an integer 

(b) an irrational number 

(c) a rational number 

(d) none of these

Answer 1

Let √2 is a rational number. 

∴ √2 = p/q , where p and q are some integers and HCF(p,q) = 1 ….(1) 

⇒ √2q = p 

⇒ (√2q) ² = p² 

⇒2q² = p² 

⇒ p² is divisible by 2 

⇒ p is divisible by 2 …..(2)

Let p = 2m, where m is some integer.

From (2) and (3), 2 is a common factor of both p and q, which contradicts (1). 

Hence, our assumption is wrong. 

Thus, √2 is an irrational number. 

Hence, the correct answer is option (b).