Question

Prove that 3+2root5 is irrational​

Answer 1

Answer:

we know that $\sqrt{5$ is an irrational no.

let 3+2$\sqrt{5}$ be a rational no. ie. in the form of a/b

so,3+2$\sqrt{5}$ =a/b

=>2$\sqrt{5}$=a/b - 3

=>$\sqrt{5}$=(a/b - 3)/2

now clearly RHS is rational, but we know that $\sqrt{5}$ is irrationa.

therefore our assumption is wrong and 3+2$\sqrt{5}$ is an irrational no.

                  hence prooved