Question

Given that root 2 is irrational, prove the (5+3 root 2) is an irrational numbers

Answer 1

Hope it helps you..

Answer 2

Heya

Given : √2 is irrational

Let (5+3√2) be a rational number

(5+3√2) = p/q where p,q are integers and q isn't equal to 0

3√2=(p-5q)/q

√2 = (p-5q)/3q

p, q are integers, so (p-5q)/3q is a rational number

As LHS= RHS, √2 becomes rational

This contradicts the fact that √2 is irrational.(given)

This contradiction arose because of our wrong assumption.

Therefore, (5+3√2) is irrational

Hope it helps!