Question

Given that √2 is irrational, prove that (5+3√2) is an irrational number.

Answer 1

let the rational number be a.
a=5+3√2
a-5/3=√2
a is a rational number,5 is a rational number,3 is a rational number.
a-5/3 is a rational number
√2 is a rational number
but it is given that√2 is a irrational number.
this contradicts the fact that a is a rational number.
our assumption is wrong.
therefore,5+3√2is a irrational number.