\[\sqrt[3]{729}\]

\[=\sqrt[3]{9\times9\times9}\]

\[=9\]

\[\sqrt{81}+\sqrt{64}\]

\[=\left(\sqrt{9\times9}\right)+\left(\sqrt{8\times8}\right)\]

\[=9+8\]

\[=17\]

\[\sqrt[3]{216}+\sqrt[3]{64}=\]

\[\left(\sqrt[3]{6\times6\times6}\right)+\left(\sqrt[3]{4\times4\times4}\right)\]

\[=6+4\]

\[=10\]

\[=\frac{\sqrt{80\times 80}}{\sqrt{40\times 40}}\]

\[=\frac{80}{40}\]

\[=\frac{8}{4}\]

\[=2\]

\[\sqrt{325}\]

\[=\sqrt{5\times5\times13}\]

\[=5\sqrt{13}\]

\[\frac{1}{\sqrt{3}}\times \sqrt{48}\]

\[=\frac{1}{\sqrt{3}}\times \sqrt{2\times 2\times 2\times 2\times 3}\]

\[=\frac{1}{\sqrt{3}}\times \sqrt{2^2\times 2^2\times 3}\]

\[=\frac{1}{\sqrt{3}}\times 2^2\sqrt{3}\]

\[=2^2\]

\[=4\]

\[\left(\frac{\sqrt{10000}}{\sqrt{100}}\right)^2\]

\[=\left(\frac{\sqrt{100\times 100}}{\sqrt{10\times 10}}\right)^2\]

\[=\left(\frac{100}{10}\right)^2\]

\[=\left(10\right)^2\]

\[=100\]

\[\frac{\left(\sqrt{100}+\sqrt{81}+\sqrt{64}+\sqrt{49}+\sqrt{36}\right)}{40}\]

\[=\frac{\left(\sqrt{10^2}+\sqrt{9^2}+\sqrt{8^2}+\sqrt{7^2}+\sqrt{6^2}\right)}{40}\]

\[=\frac{\left(10+9+8+7+6\right)}{40}\]

\[=\frac{40}{40}\]

\[=1\]

\[\left[\frac{2\sqrt{3}}{\sqrt{12}}\times \frac{\sqrt{18}}{3\sqrt{2}}\right]\]

\[=\left[\frac{2\sqrt{3}}{\sqrt{2\times 2\times 3}}\times \frac{\sqrt{3\times 3\times 2}}{3\sqrt{2}}\right]\]

\[=\left[\frac{2\sqrt{3}}{2\sqrt{3}}\times \frac{3\sqrt{2}}{3\sqrt{2}}\right]\]

\[=1\times 1\]

\[=1\]

Let the age of Manoj be \[x\]

Then, age of Alok will be \[2x\]

According to the question,

\[x\times 2x=800\]

\[\Rightarrow 2x^2=800\]

\[\Rightarrow x^2=400\]

\[\Rightarrow x=\sqrt{400}\]

\[\Rightarrow x=20\]

\[\therefore\] age of Alok = \[2x =2\times20=40\] years

Let the width be \[x\]

Then, the length will be \[3x\]

According to the question,

\[x \times 3x = 1200 m^2\]

\[\implies 3x^2 =1200m^2\]

\[\implies x^2=\frac{1200m^2}{3}\]

\[\implies x=\sqrt{400m^2}\]

\[\implies x=20m\]

\[\therefore\] the width is = 20m

and length \[=3 \times\] width

\[=3\times 20m=60m\]

\[\sqrt{\frac{x}{9}}=3\]

\[\Rightarrow \sqrt{x}=3\times 3\]

\[\Rightarrow x=9^2\]

\[=81\]

\[\sqrt{\frac{x^2}{100}}=\sqrt{\frac{y^2}{400}}\]

\[\Rightarrow \frac{x}{10}=\frac{y^{ }}{20}\]

\[\Rightarrow \frac{x}{y}=\frac{10}{20}\]

\[=\frac{1}{2}\]

\[=1:2\]

\[\frac{\sqrt{\left(\sqrt{\left(\sqrt{2}\right)^2}\right)^{^2}}}{x^2}\]

\[=\frac{\sqrt{\left(\sqrt{2}\right)^2}^{^{ }}}{(\sqrt{2})^2}\]

\[=\frac{\sqrt{2}}{2}\]

\[=\frac{\sqrt{2}}{\sqrt{2\times 2}}\]

\[=\frac{1}{\sqrt{2}}\]

\[x+x^2+\sqrt{x}+\frac{1}{\sqrt{x}}\]

\[=1+1^2+\sqrt{1}+\frac{1}{\sqrt{1}}\]

\[=1+1+1+1\]

\[=4\]