Question

prove that root 3 is irrational

Answer 1

let root 3 is rational no.,where root 3 =p/q and q is not equal to 0.
root3= p/q
3=p square/q square
3q square = p square
we see that p square divides 3q squre
let q square be 3m
now...
3m =(3p )square
3m =9p
m =3
so 3 is not rational no.
became both have comman factors
hence it is a irrational no.
hope this will help you. .

Answer 2

Suppose root 3 is irrational
Therefore,root 3 is in p/q form where p and q are co-prime no.
Now squaring,
3=p^2/q^2
q^2=p^2/3(since,let p be a prime no. Of a^2/p =a/p)
= p/3-(1)6
p=3m
Put the value p=3m in eqa.1
(1)3=(3m)^2/q^2
3=9m^2/q^2
q^2 =3m^2
Therefore it contradicts our fact that p and q are the co -prime .
Therefore our assumption is wrong .
So ,root 3 is irrational