[tex]\bf \sqrt{10a}\times \sqrt{30a}\implies \sqrt{10a\times 30a}\implies \sqrt{10\cdot 30\cdot a\cdot a}\implies \sqrt{300a^2}
\\\\\\
\begin{cases}
300=2\cdot 2\cdot 3\cdot 5\cdot 5\\
\qquad 2^2\cdot 3\cdot 5^2\\
\qquad (2\cdot 5)^2\cdot 3\\
\qquad 10^2\cdot 3
\end{cases}\implies \sqrt{10^2\cdot 3\cdot a^2}\implies 10a\sqrt{3}[/tex]
