Question

show that root 3 + 2root5 is irrational

Answer 1

let us assume to a contrary that 3+2 (root5) is a rational number

therefore 3+2(root 5) = a/b

= root 5 =a/2b -3

, a/2b-3 is rational. therefore root 5 is rational.

it contradicts the fact that root 5 is irrational. therefore our assumption is wrong.

therefore 3+2(root 5) is irrational.

Hope it helps you buddy