4.2 The root function

One useful property of the root function is that any root of aa multiplied by bb is the same as the root of aa multiplied by the square root of bb.

In the case where we are interested in the square root, we have

ab=ab\sqrt{ab}=\sqrt{a}\cdot\sqrt{b} (4.5)

This makes it possible to simplify expressions inside square root, for example

8\displaystyle\sqrt{8} =42\displaystyle=\sqrt{4}\sqrt{2} (4.6)
=22\displaystyle=2\sqrt{2} (4.7)