Question

( 4 - 3sqrt2 )^2 + 8sqrt34 - 24sqrt2 = ?

Answer 1

$(4-3\sqrt2)^2+8\sqrt{34-24\sqrt2}\\ 16-24\sqrt2+18+8\sqrt{16-2\cdot4\cdot3\sqrt2+18}\\ 34-24\sqrt2+8\sqrt{(4-3\sqrt2)^2}\\\\ 4 \vee 3\sqrt2\\ 16 \vee 9\cdot 2\\ 16 \ \textless \ 18\\ 4 - 3\sqrt2 \ \textless \ 0\\ \sqrt{(4-3\sqrt2)^2} = \sqrt{(3\sqrt2-4)^2} = 3\sqrt2-4\\\\ 34-24\sqrt2+8(3\sqrt2 - 4)\\ 34 - 24\sqrt2+24\sqrt2-32 = 2$