Question

-5sqrt2(-4sqrt6)

Answer 1

\[-5\sqrt{2}\times (-4\sqrt{6})=(-5)\times (-4)\times \sqrt{2\times 6}=20\sqrt{12}\]

Answer 2

and since \(\sqrt{12}=\sqrt{4}\times \sqrt{3}=2\sqrt{3}\) you can write
\[20\sqrt{12}=40\sqrt{3}\]

Answer 3

nothing magic here. you can change the order of multiplication.
and you can use the idea that
\[ \sqrt{a}\sqrt{b}= \sqrt{ab}\]
the only nit I have with sat's answer is I would not multiply 2*6 to get 12. I would factor 6 to get 2*2*3 and look for pairs to pull out of the square root.

Answer 4

good point