Question

Without using tables find the value of (2+√6)^6+(2-√3)^6

Answer 1

Note that the expansion of (a+b)^6 is
a^6 + 6a^5b + 15a^4b^2 + 20a^3b^3 + 15a^2b^4 + 6ab^5 + b^6

So just plug in your numbers.

Too bad it's not (2+√3)^6 since that would make all the odd powers of b (those pesky roots) go away. Check to be sure that's not what you meant.

Answer 2

Elementary trigonometry