From Förberedande kurs i matematik 1

We start by looking at the one part of the expression, \displaystyle \sqrt{16}. This root can be simplified since \displaystyle 16=4\centerdot 4=4^{2} which gives that \displaystyle \sqrt{16}=\sqrt{4^{2}}=4 and the whole expression becomes

\displaystyle \sqrt{16+\sqrt{16}}=\sqrt{16+4}=\sqrt{20}

Can \displaystyle \sqrt{20} be simplified? In order to answer this, we split \displaystyle \text{2}0 up into integer factors,

\displaystyle 20=2\centerdot 10=2\centerdot 2\centerdot 5=2^{2}\centerdot 5

and see that \displaystyle \text{2}0\text{ } contains the square \displaystyle \text{2}^{\text{2}} as a factor and can therefore be taken outside the root sign,

\displaystyle \sqrt{20}=\sqrt{2^{2}\centerdot 5}^{2}=2\sqrt{5}