## anonymous 4 years ago 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

1. anonymous

lwh

2. anonymous

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

3. anonymous

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: $38(\sqrt{15}-\sqrt{2})=38\sqrt{15}-38\sqrt{2}$