Question

How do I express the volume of the rectangular prism in simplest radical form. L: 5√2 + 2√3, w: √15 - √2 and h: 5√2 - 2√3. The answer has to be: 38√15 - 38√2

Answer 1

lwh

Answer 2

yes, I know. but how do I multiply the radicals? I got -15√1365 but it's wrong.

Answer 3

Look at the length and the height; this is a difference of 2 squares:
\[(5\sqrt{2}+2\sqrt{3})(5\sqrt{2}-2\sqrt{3})=(5\sqrt{2})^2-(2\sqrt{3})^2=50-12=38\]
Then the other dimension:
\[38(\sqrt{15}-\sqrt{2})=38\sqrt{15}-38\sqrt{2}\]