Question

(5√2-15√5)(4√2+12√5)
I got
(√27+√230)(√18+√149)
√486+√4023+√4140+√34,270
Is this the final answer or can it be simplified...

Answer 1

\[\begin{align}
(5\sqrt{2}-15\sqrt{5})(4\sqrt{2}+12\sqrt{5})&=(5\sqrt{2})(4\sqrt{2})+(5\sqrt{2})(12\sqrt{5})\\
&-(15\sqrt{5})(4\sqrt{2})-(15\sqrt{5})(12\sqrt{5})\\
&=(20*\sqrt{2}*\sqrt{2})+(60*\sqrt{2}*\sqrt{5})\\
&-(60*\sqrt{5}*\sqrt{2})-(180*\sqrt{5}*\sqrt{5})\\
&=(20*2)+(60*\sqrt{10})-(60*\sqrt{10})-(180*5)\\
&=(40)-(900)\\
&=-860
\end{align}\]