[tex]\bf 6\sqrt{500}-3\sqrt{20}+\sqrt{18}\qquad
\begin{cases}
500=2\cdot 2\cdot 5\cdot 5\cdot 5\\
\qquad 2^2\cdot 5^2\cdot 5\\
\qquad (2^2\cdot 5^2)5\\
\qquad (2\cdot 5)^2 5\\
\qquad 10^2\cdot 5\\
20=2\cdot 2\cdot 5\\
\qquad 2^2\cdot 5\\
18=2\cdot 3\cdot 3\\
\qquad 2\cdot 3^2
\end{cases}
\\\\\\
6\sqrt{10^2\cdot 5}-3\sqrt{2^2\cdot 5}+\sqrt{2\cdot 3^2}\implies 6\cdot 10\sqrt{5}-3\cdot 2\sqrt{5}+3\sqrt{2}
\\\\\\
\stackrel{like~terms}{60\sqrt{5}-6\sqrt{5}}+3\sqrt{2}\implies 54\sqrt{5}+3\sqrt{2}[/tex]
