Giải thích các bước giải:
$G=\dfrac{\sqrt[4]{49+20\sqrt{6}}+\sqrt[4]{49+20\sqrt{6}}}{2\sqrt{3}}$
$= \dfrac{\sqrt[4]{(5+2\sqrt{6})^2}+\sqrt[4]{(5-2\sqrt{6})^2}}{2\sqrt{3}}$
$= \dfrac{\sqrt{5+2\sqrt{6}}+\sqrt{5-2\sqrt{6}}}{2\sqrt{3}}$
$= \dfrac{\sqrt{(\sqrt{2}+\sqrt{3})^2}+\sqrt{(\sqrt{2}-\sqrt{3})^2}}{2\sqrt{3}}$
$= \dfrac{|\sqrt{2}+\sqrt{3}|+|\sqrt{2}-\sqrt{3}|}{2\sqrt{3}}$
$= \dfrac{\sqrt{2}+\sqrt{3}-\sqrt{2}+\sqrt{3}}{2\sqrt{3}}$
$=\dfrac{2\sqrt{3}}{2\sqrt{3}}$
$=1$
$\text{Vậy $G=\dfrac{\sqrt[4]{49+20\sqrt{6}}+\sqrt[4]{49+20\sqrt{6}}}{2\sqrt{3}}=1$}$
Học tốt!!!
