Question

Prove that $5+\sqrt{3}$ is irrational.

Answer 1

In $5+\sqrt{3}$, the number $\sqrt{3}$ is an irrational number.

Also, $5$ is a rational number.

We know, the sum of a rational number and an irrational number is always an irrational number.

Therefore, since $\sqrt{3}$ is an irrational number, $5+\sqrt{3}$ is also an irrational number.

$\therefore$ Hence proved.