POW #2: Integer in Disguise

Show that $\sqrt[3]{7+5\sqrt{2}}+\sqrt[3]{7-5\sqrt{2}}$ is an integer.

(Of course, work done by computer or calculator will not be accepted. You must prove algebraically that the number above is an integer. Show all work!)


Return to Laura Taalman, Burruss 127, by 2/11/04.