Question : If $x=\sqrt{64}+\sqrt{121}-\sqrt{169}$, then find the value of $x^2$.

Option 1: 16

Option 2: 25

Option 3: 36

Option 4: 48

Question : If $x^4+\frac{16}{x^4}=15617, x>0$, then find the value of $x+\frac{2}{x}$.

Option 1: $\sqrt{121}$

Option 2: $\sqrt{129}$

Option 3: $\sqrt{123}$

Option 4: $\sqrt{127}$

Question : If $x^2-\frac{1}{x^2}=4 \sqrt{2}$, what is the value of $x^4-\frac{1}{x^4}?$

Option 1: $16 \sqrt{2}$

Option 2: $8\sqrt{2}$

Option 3: $24 \sqrt{2}$

Option 4: $32 \sqrt{2}$

Question : If $\left(x^2+\frac{1}{x^2}\right)=7$, and $0<x<1$, find the value of $x^2-\frac{1}{x^2}$.

Option 1: $3 \sqrt{5}$

Option 2: $4 \sqrt{5}$

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

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

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 : If $\frac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=3$, what is the value of $x$?

Option 1: $\frac{5}{2}$

Option 2: $\frac{25}{3}$

Option 3: $4$

Option 4: $3$