**Solution:**

Let us assume, to the contrary that 5 + 3√2 is rational.

So, we can find coprime integers a and b(b ≠ 0)

such that 5 + 3√2 = a/b

=> 3√2 = a/b - 5

=> √2 = (a - 5b)/3b

Since a and b are integers, (a - 5b)/3b is rational.

So, √2 is rational.

But this contradicts the fact that √2 is irrational.

**Hence, **5 + 3√2** is irrational.**