Question

Show that the following numbers are irrational . 1) root 2 , 2) root 3 , 3) root 5 , 4) 3root 2 5)root 2 +root 5

Answer 1

proof by contradiction ex:

let us assume √2 is rational

so it can be written in p/q form

√2=p/q

p

2 =(p/q)^2

2q^2=p^2

2q is divisible by p

k^2=(2q)^2

so p and q are not co primes hence √2 is irrational

hence our assumption is wrong

Hence Proved

:)