Which statement correctly justifies that $3\sqrt{2}$ is irrational?

Question

Accepted Answer

A. If $3\sqrt{2}$ were rational, then dividing by the non-zero rational number 3 would make $\sqrt{2}$ rational, which is impossible.

Assume $3\sqrt{2}$ is rational. Since 3 is a non-zero rational number, dividing by 3 would imply $\sqrt{2}$ is rational. But $\sqrt{2}$ is irrational, so the assumption is false and $3\sqrt{2}$ is irrational.

Answer

$3\sqrt{2}$ is irrational because 3 is prime.

Answer

$3\sqrt{2}$ is irrational because all products are irrational.

Answer

$3\sqrt{2}$ is irrational because $\sqrt{2}>3$.