32 is divisable by 2 so √16*√2.
It is not the 2 that is important here. It is the 16
32=16*2
If you want to simplify a surd you have to look for a squared number that goes into it.
squared numbers are (don't worry about 1, it is not helpful)
$$\\1^1=1, \;2^2=4,\;3^2=9,\;4^2=16\;etc\\\\
1,4,9,16,25,26,49,etc$$
$$\begin{array}{rlll}
\sqrt{32}&=&\sqrt{16\times2}\\\\
&=&\sqrt{16}\times \sqrt2&\\\\
&=&4\sqrt2&\\\\
\end{array}$$
so it is pulling out the square number that is the important bit!