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$\left|\begin{array}{ccc}\sqrt{3} & 2 \sqrt{5} & \sqrt{5} \\ \sqrt{15} & 5 & \sqrt{10} \\ 3 & \sqrt{15} & 5\end{array}\right|=$
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The correct answer is:
$15 \sqrt{2}-25 \sqrt{3}$
$\left|\begin{array}{ccc}\sqrt{3} & 2 \sqrt{5} & \sqrt{5} \\ \sqrt{15} & 5 & \sqrt{10} \\ 3 & \sqrt{15} & 5\end{array}\right|$
$\begin{aligned} & =\sqrt{3}(25-\sqrt{150})-2 \sqrt{5}(5 \sqrt{15}-3 \sqrt{10})+\sqrt{5}(15-15) \\ & =25 \sqrt{3}-15 \sqrt{2}-50 \sqrt{3}+30 \sqrt{2} \\ & =15 \sqrt{2}-25 \sqrt{3}\end{aligned}$
$\begin{aligned} & =\sqrt{3}(25-\sqrt{150})-2 \sqrt{5}(5 \sqrt{15}-3 \sqrt{10})+\sqrt{5}(15-15) \\ & =25 \sqrt{3}-15 \sqrt{2}-50 \sqrt{3}+30 \sqrt{2} \\ & =15 \sqrt{2}-25 \sqrt{3}\end{aligned}$
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