[tex]\bf \sqrt{75x^5y^8}\qquad
\begin{cases}
75=3\cdot 25\\
\qquad 3\cdot 5^2\\
x^5=x^{4+1}\\
\qquad x^4x^1\\
\qquad (x^2)^2x\\
y^8=y^{4\cdot 2}\\
\qquad (y^4)^2
\end{cases}\implies \sqrt{3\cdot 5^2\cdot (x^2)^2x(y^4)^2}
\\\\\\
5x^2y^4\sqrt{3x}[/tex]
