$$\begin{aligned} x = 3 + 2\sqrt{2}, \text{ then the value of }\\ (\sqrt{x} - \frac{1}{\sqrt{x}}) \end{aligned}$$

Answer: Option B

Explanation:

Clue:

$$\begin{aligned} (\sqrt{x} - \frac{1}{\sqrt{x}})^2 = x + \frac{1}{x} - 2 \ \end{aligned}$$
Now put the value of x to calculate the answer :)

Answer: Option C

Answer: Option D

Explanation:

Lets assume,

$$\begin{aligned} \left(25 \right)^{7.5} \times \left(5 \right)^{2.5} \div \left(125 \right)^{1.5} = 5^x \\ \text{then, } \frac{ \left( 5^2 \right)^{7.5} \times \left(5 \right)^{2.5} }{\left(5^3 \right)^{1.5} } = 5^x \\ => \text{then, } \frac{ \left( 5^{15} \right) \times \left(5^{2.5} \right) }{\left(5^{4.5} \right) } = 5^x \\ => 5^x = 5^{15 + 2.5 - 4.5} \\ => 5^x = 5^{13} \\ \text{Hence, } x = 13 \end{aligned}$$

Answer: Option B

Explanation:

$$\begin{aligned} = (256)^{\frac{5}{4}} = (4^4)^{\frac{5}{4}} = 4^5 = 1024 \end{aligned}$$

Answer: Option D

Explanation:

$$\begin{aligned} = \frac{(10)^{150}}{(10)^{146}} = 10^4 = 10000 \end{aligned}$$