Đáp án:
$1+\sqrt[]{2}$
Giải thích các bước giải:
$\dfrac{\sqrt[]{2}+\sqrt[]{3}+\sqrt[]{6}+\sqrt[]{8}+\sqrt[]{16}}{\sqrt[]{2}+\sqrt[]{3}+2}$
$=\dfrac{\sqrt[]{2}+\sqrt[]{3}+\sqrt[]{6}+\sqrt[]{8}+\sqrt[]{4^2}}{\sqrt[]{2}+\sqrt[]{3}+2}$
$=\dfrac{\sqrt[]{2}+\sqrt[]{3}+\sqrt[]{6}+\sqrt[]{8}+4}{\sqrt[]{2}+\sqrt[]{3}+2}$
$=\dfrac{\sqrt[]{2}+\sqrt[]{3}+\sqrt[]{6}+\sqrt[]{8}+2+2}{\sqrt[]{2}+\sqrt[]{3}+2}$
$=\dfrac{\sqrt[]{2}+\sqrt[]{3}+2+\sqrt[]{2}.\sqrt[]{3}+2\sqrt[]{2}+2}{\sqrt[]{2}+\sqrt[]{3}+2}$
$=\dfrac{\sqrt[]{2}+\sqrt[]{3}+2+\sqrt[]{2}(\sqrt[]{3}+\sqrt[]{2}+2)}{\sqrt[]{2}+\sqrt[]{3}+2}$
$=\dfrac{(\sqrt[]{2}+\sqrt[]{3}+2)+(1+\sqrt[]{2})}{\sqrt[]{2}+\sqrt[]{3}+2}$
$=1+\sqrt[]{2}$
