Answer
$100-3\sqrt2-10\sqrt3+10\sqrt6$
Work Step by Step
Recall:
$(a+b)(c+d) = a(c+d) + b(c+d)$
Use the rule above to obtain:
\begin{align*}
&=10(10-\sqrt3) +\sqrt{6}(10-\sqrt3)\\
&=10(10) - 10(\sqrt3)+\sqrt6(10)-\sqrt6(\sqrt3)\\
&=100-10\sqrt3+10\sqrt6-\sqrt{18}\\
&=100-10\sqrt3+10\sqrt6-\sqrt{9(2)}\\
&=100-10\sqrt3+10\sqrt6-\sqrt{3^2(2)}\\
&=100-10\sqrt3+10\sqrt6-3\sqrt2\\
&=100-3\sqrt2-10\sqrt3+10\sqrt6
\end{align*}
