[tex]\bf \sqrt{200}-\sqrt{32}\quad
\begin{cases}
200=2\cdot 2\cdot 2\cdot 5\cdot 5\\
\qquad 2^2\cdot 2\cdot 5^2\\
\qquad (2\cdot 5)^2\cdot 2\\
\qquad (10)^2\cdot 2\\
32=2\cdot 2\cdot 2\cdot 2\cdot 2\\
\qquad 2^2\cdot 2^2\cdot 2\\
\qquad (2\cdot 2)^2\cdot 2\\
\qquad (4)^2\cdot 2
\end{cases}\implies \sqrt{10^2\cdot 2}-\sqrt{4^2\cdot 2}
\\\\\\
10\sqrt{2}-4\sqrt{2}\implies 6\sqrt{2}\implies 6\cdot 2^{\frac{1}{2}}[/tex]
