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

\begin{equation} \sqrt {ab} = \sqrt {a} \cdot \sqrt {b} \end{equation}

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}