Question

prove that √3 is irrational.​

Answer 1

Answer:

let √3 is a rational no.

we can say that p/q = √3 (hcf = 1)

p/q = √3

squaring both sides

p^2/q^2 = 3

p^2/3 = q^2 ----- (1)

p^2 is divisible by 3 & p is also divisible by 3.

let p = 3m

put in (1) eq.

9m^2/3 = q^2

m^2 = q^2/ 3

q^2 is divisible by 3 & q is also divisible by 3

but our assumption is wrong. its hcf = 1. so it is contradicted that √3 is an irrational no.