Question

prove √n is irrational number

Answer 1

let √n be rational no.
p/q=√n(p and q are co-prime no.s)co-prime nos are the number which has factor as 1)
squaring both the sides 
p²/q²=n
p²=nq².....1
p²÷n=q²
p÷n(using therum a²÷p gives a÷p).....2
let p=nc(c is any positive integer)
squaring both sides
p²=n²c²
from1
nq²=n²c²
q²=nc²
q²÷n=c²
q÷n,using the above theorum...3

from 2 and 3  
we can say that p and q are not co prime numbers because they have factor as n
therefore, this contradiction arises due to our wrong assmption


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