prove that √3 is irrational.
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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.
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