My book says $\sqrt{18}$ is a pure surd. Is it correct or a misprint?

Question

My book says $\sqrt{18}$ is a pure surd. Is it correct or a misprint?

I think $\sqrt{18}$ can be expressed as $3\sqrt{2}$, which I think is a mixed surd. Am I wrong?

Answer 1

As far as I can tell, being a pure surd or otherwise is not a property of the number, but a property of the way it is written. The numerical expression $3\sqrt2$ is a mixed surd and the expression $\sqrt{18}$ is a pure surd, despite them representing the same real number.

Answer 2

It is true that $\sqrt{18}=3\sqrt{2}$. However, to say it is a pure surd or a mixed surd, we consider the expression as whole. If it is of the form "$\sqrt{\text{rational}}$" then it is pure, and if it is of the form "$\text{rational}\sqrt{\text{rational}}$", then it is a mixed surd.

What I think, you understood that $\sqrt{\text{prime}}$ is pure, and that $\sqrt{\text{composite}}$ is mixed, but that is untrue.