[tex]\bf \sqrt{200y^4}\qquad
\begin{cases}
200=2\cdot 2\cdot 2\cdot 5\cdot 5\\
\qquad 2^2\cdot 2\cdot 5^2\\
y^4=y^{2+2}\\
\qquad y^2\cdot y^2\\
\qquad (y^2)^2
\end{cases}\implies \sqrt[2]{2^2\cdot 2\cdot 5^2\cdot (y^2)^2}
\\\\\\
2\cdot 5\cdot y^2\sqrt{2}\implies 10y^2\sqrt{2}[/tex]
