Đáp án:
Giải thích các bước giải:
M = $\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}$
$\dfrac{1}{M}$ = $\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}$
$\dfrac{1}{M}$ = $\dfrac{\sqrt{2}+\sqrt{3}+2+2+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}$ $\dfrac{1}{M}$ = $\dfrac{(\sqrt{2}+\sqrt{3}+2)+\sqrt{2}(\sqrt{2}+\sqrt{3}+2)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}$
$\dfrac{1}{M}$ = $\dfrac{\sqrt{2}+\sqrt{3}+2}{\sqrt{2}+\sqrt{3}+2}$ + $\dfrac{\sqrt{2}(\sqrt{2}+\sqrt{3}+2)}{\sqrt{2}+\sqrt{3}+2}$
$\dfrac{1}{M}$ = 1 + $\sqrt{2}$
$M$ = $\dfrac{1}{1 + \sqrt{2}}$
$O$ = $\sqrt{72}$ + 2$\sqrt{27}$ - 3$\sqrt{18}$ - 4$\sqrt{12}$ + $\dfrac{2}{2-\sqrt{3}}$
= 6$\sqrt{2}$ + 6$\sqrt{3}$ - 9$\sqrt{2}$ - 8$\sqrt{3}$ + 4 + 2$\sqrt{3}$
= $\sqrt{2}$ $(6 - 9)$ + $\sqrt{3}$ $(6 - 8 + 2)$ + 4
= - 3$\sqrt{2}$ + 4
= 4 - 3$\sqrt{2}$
