Question

Show that 7 minus root 2 5 is irrational give that root 5 is irrational

Answer 1

let √5 be a rational no. then
√5=p/q where p is an integer and q is not equal to 0
√5q=p ; squaring both side
5q(square)=p(square) - (1)
I.e. 5 is divisible by p(square)
5 is divisible by p
let take another variable x now
5x=p ;squaring both sides
25x(square)=p(square). - (2)
I.e. 25 is also divisible by p
by 1 and 2 we get
25x(square) =5q(square)
q = 5x
therefore our assumption is wrong
so, √5 is an rational no.