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: $2 \sqrt{2}+1$

Question : If $\frac{22 \sqrt{2}}{4 \sqrt{2}-\sqrt{3+\sqrt{5}}}=a+\sqrt{5} b$, with $a, b>0$, then what is the value of $(a b):(a+b)$?

Option 1: 7 : 8

Option 2: 7 : 4

Option 3: 4 : 7

Option 4: 8 : 7

Question : The value of $5–\frac{8+2\sqrt{15}}{4}–\frac{1}{8+2\sqrt{15}}$ is equal to:

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

Option 2: $1$

Option 3: $\frac{2}{3}$

Option 4: $\frac{1}{2}$

Question : The square root of $\frac{2+\sqrt{3}}{2}$ is:

Option 1: $\pm \frac{1}{\sqrt{2}}(\sqrt{3}+1)$

Option 2: $\pm \frac{1}{2}(\sqrt{3}-2)$

Option 3: $\text{none}$

Option 4: $\pm \frac{1}{2}(\sqrt{3}+1)$