Question : The value of $\sqrt{–\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}$ is:

Option 1: 2

Option 2: 4

Option 3: $\pm 2$

Option 4: –2

Question : If $(x+\frac{1}{x})=6$ and $x>1$, find the value of $(x^2–\frac{1}{x^2})$.

Option 1: $18 \sqrt{2}$

Option 2: $30 \sqrt{2}$

Option 3: $24 \sqrt{2}$

Option 4: $12 \sqrt{10}$

Question : If $a = 64$ and $b = 289$, then the value of $\sqrt{\sqrt{\sqrt{a}+\sqrt{b}}-\sqrt{\sqrt{b}-\sqrt{a}}}$ is:

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

Option 2: $2$

Option 3: $4$

Option 4: $–1$

Question : If $x=\sqrt{–\sqrt{3}+\sqrt{3+8 \sqrt{7+4 \sqrt{3}}}}$ where $x > 0$, then the value of $x$ is equal to:

Option 1: 3

Option 2: 4

Option 3: 1

Option 4: 2

Question : What is the value of $\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}–\sqrt{5}} \div \frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}–\sqrt{10}}+\frac{\sqrt{10}}{\sqrt{5}}$?

Option 1: $\sqrt{2}+2$

Option 2: $2 \sqrt{2}+2$

Option 3: $\sqrt{2}+1$

Option 4: $2 \sqrt{2}+1$