# A calculus of the absurd

#### 4.2 The root function

One useful property of the root function is that any root of $$a$$ multiplied by $$b$$ is the same as the root of $$a$$ multiplied by the square root of $$b$$.

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

$$\sqrt {ab} = \sqrt {a} \cdot \sqrt {b}$$

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

\begin{align} \sqrt {8} & = \sqrt {4}\sqrt {2} \\ & = 2\sqrt {2} \end{align}