Question : If $x=(\sqrt{6}-1)^{\frac{1}{3}}$, then the value of $\left(x-\frac{1}{x}\right)^3+3\left(x-\frac{1}{x}\right)$ is:

Option 1: $\frac{2 \sqrt{6}-6}{5}$

Option 2: $\frac{4 \sqrt{6}-6}{5}$

Option 3: $\frac{4 \sqrt{6}-6}{3}$

Option 4: $\frac{4 \sqrt{3}-6}{5}$

Question : The simplified value of $\frac{3\sqrt 2 }{\sqrt3 + \sqrt6} - \frac{4 \sqrt 3 }{\sqrt{6}+ \sqrt {2}} + \frac{\sqrt 6}{\sqrt{3}+ \sqrt 2}$ is:

Option 1: $\sqrt 2$

Option 2: $\frac{1}{\sqrt2}$

Option 3: $\sqrt 3- \sqrt 2$

Option 4: $0$

Question : The value of exponential form of $\sqrt{\sqrt{2}\sqrt{3}}$ is:

Option 1: $6$

Option 2: $6^{\frac{1}{2}}$

Option 3: $6^{-\frac{1}{2}}$

Option 4: $6^{\frac{1}{4}}$

Question : Evaluate $\sqrt{20}+\sqrt{12}+\sqrt[3]{729}-\frac{4}{\sqrt{5}-\sqrt{3}}-\sqrt{81}:$

Option 1: $\sqrt{2}$

Option 2: $\sqrt{3}$

Option 3: $0$

Option 4: $2\sqrt{2}$

Question : The value of $\frac{1}{1+\sqrt{2}+\sqrt{3}}+\frac{1}{1-\sqrt{2}+\sqrt{3}}$ is:

Option 1: $\sqrt{2}$

Option 2: $\sqrt{3}$

Option 3: $1$

Option 4: $4(\sqrt{3}+\sqrt{2})$