Why can I simplify radicals? (eg, $sqrt{153} = sqrt{3}cdot sqrt{3}cdot sqrt{17}$)

I know it might sound like a ridiculously easy question to answer, but I just can't put two and two together for some reason.

Say for example you have:
$$\sqrt{153}$$
You can break it down to
$$\sqrt{3}\cdot \sqrt{3}\cdot \sqrt{17}$$
(and of course you can further simplify it, but we'll just leave it at that for now).

Why can I do that?