Aus Online Mathematik Brückenkurs 1

The decimal number \displaystyle 0.\text{16 } can also be written as \displaystyle \text{16}\centerdot \text{1}0^{-\text{2}}\text{ } and then it is easier to see that, since \displaystyle \text{16}=\text{4}\centerdot \text{4}=\text{4}^{\text{2}}\text{ } and \displaystyle 10^{-2}=\left( 10^{-1} \right)^{2}=0.1^{2}

\displaystyle \begin{align} & \sqrt{0.16}=\sqrt{16\centerdot 10^{-2}}=\sqrt{16}\centerdot \sqrt{10^{-2}}=\sqrt{4^{2}}\centerdot \sqrt{0.1^{2}} \\ & =4\centerdot 0.1=0.4 \\ \end{align}

Another alternative is, of course, to see directly that \displaystyle 0.16=0.4\centerdot 0.4=0.4^{2}, and then that \displaystyle \sqrt{0.16}=\sqrt{0.4^{2}}=0.4