\(=\dfrac{\sqrt{2}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}+\dfrac{\sqrt{2}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}\\ =\sqrt{2}+\sqrt{2}=2\sqrt{2}\)

\(\dfrac{\sqrt[]{10}-\sqrt[]{2}}{\sqrt[]{5}-1}+\dfrac{2-\sqrt[]{2}}{\sqrt[]{2}-1}\)

\(=\dfrac{\sqrt[]{2}\left(\sqrt[]{5}-1\right)}{\sqrt[]{5}-1}+\dfrac{\sqrt[]{2}\left(\sqrt[]{2}-1\right)}{\sqrt[]{2}-1}\)

\(=\sqrt[]{2}+\sqrt[]{2}=2\sqrt[]{2}\)

\(1+2+2^2+2^3+...+2^n=357680\)

\(\Leftrightarrow2\cdot\left(1+2+2^2+...+2^n\right)=2\cdot357680\)

\(\Leftrightarrow2+2^2+2^3+2^4+...+2^{n+1}=2\cdot357680\)

\(\Leftrightarrow\left(2+2^2+...+2^{n+1}\right)-\left(1+2+2^2+...+2^n\right)=2\cdot357680-357680\)

\(\Leftrightarrow\left(2-2\right)+\left(2^2-2^2\right)+...+\left(2^n-2^n\right)+\left(2^{n+1}-1\right)=357680\)

\(\Leftrightarrow2^{n+1}-1=357680\)

\(\Leftrightarrow2^{n+1}=357681\)

Xem lại đề 

\(1+2+2^2+2^3+...+2^n=357680\)

\(\Rightarrow\dfrac{2^{n+1}-1}{2-1}=357680\)

\(\Rightarrow2^{n+1}=357680+1\)

\(\Rightarrow2^{n+1}=357681\Rightarrow n+1=\sqrt[]{357681}\Rightarrow n=\sqrt[]{357681}-1\)

Ta có :

$\begin{array}{c}\angle ABC=90°-60°=30°,\angle ACB=90°+30°=120°\\ \Rightarrow \angle CAB=180°-30°-120°=30°\Rightarrow \angle ABC=\angle CAB\end{array}$

$\Rightarrow \Delta CAB$ cân tại C$\Rightarrow AC=BC=100m$

Ta có:$h=AC.\sin 30°=100.\frac{1}{2}=50m$