Question

If √2 is an irrational number, then prove the following • √2-5 is irrational.

Answer 1

Answer:

let us assume that root 2 - 5 is a rational no.

so root 2 - 5 = p/q , where p and q are some integers and q # 0

=> root 2 = p- 5q / q

this show that root 2 is rational no. because p , 5 and q are some integers

but we know that root 2 is irrational no.

=> root 2 - 5 is irrational no.

hence proved.