let us assume some rational number x which is equal to 5 + 3√2.

Step-by-step explanation:

if x = 5 + 3√2 is rational number then,

x - 5 = 3√2 will be a rational number;

(x - 5) / 3 = √2 will also be a rational number.

but according to our initial supposition, √2 is an irrational number,

So, (5 + 3√2) will also be an irrational number.

Answer:

5 + 3√2 is irrational.

Step-by-step explanation:

Let us assume the contrary. That contradicts the fact that √2 is irrational. The contradiction is because of the incorrect assumption that (5 + 3√2) is rational. So, 5 + 3√2 is irrational