Question

prove that √2 is irrational

Answer 1

hope it helps you..........

Answer 2

Hey!!!!

By the method of Contradiction,

let √2 be a rational number

Thus √2 = p/q where p,q are integers and HCF(p,q) = 1

=> p = √2 q

Square both sides

=> p² = 2q² --------- equation 1
=> p² is divisible by 2
=> p is also divisible by 2

let p = 2m

Square both sides

=> p² = 4m²
=> 2q² = 4m² ( from equation 1 )
=> q² = 2m²
=> q² is divisible by 2
=> Thus q is also divisible by 2

Here HCF(p,q) = 2
but it should be HCF(p,q) = 1

This is contradictory to our assumption that √2 is rational.

Thus √2 is an irrational number.

HENCE PROVED