Question

$\sqrt{4+2 \sqrt{3} } = ?$
Spuneti-mi va rog cum se ajunge la rezultatul $\sqrt{3+1}$ ca nu inteleg nimica , v-as fi recunoscator :|.

Answer 1

$\sqrt{4+2\sqrt3}=\sqrt{3+2\sqrt3+1}=\sqrt{(\sqrt3)^2+2\sqrt3+1^2}=\sqrt{(\sqrt3+1)^2}=$

$=|\sqrt3+1|=\sqrt3+1$

Answer 2

$\sqrt{ {4} +2 \sqrt{3}} = \\ \sqrt{4+ \sqrt{12} } \\A=4 \\ B=12 \\ C ^{2} =A ^{2}-B \\ \\ C^{2}=4^{2}-12 =16-12=4\\C^{2}=4 => C=2 \\ \sqrt { \frac{A+C}{2} } + \sqrt { \frac {A-C}{2}}= \\ \sqrt { \frac{4+2}{2}} + \sqrt{ \frac {4-2}{2} }= \\ \sqrt { \frac {6}{2}} + \sqrt { \frac {2}{2}}= \sqrt3 + 1$