https://file.aiquickdraw.com/mathbot/file/17277074810299pbnzk2z.jpg

Let's evaluate the expressions step by step to find the correct one. 

### A:
\[
\sqrt{\frac{8}{2}} + \sqrt{\frac{16}{4}} + \sqrt{\frac{24}{6}}
\]

- \(\sqrt{\frac{8}{2}} = \sqrt{4} = 2\)
- \(\sqrt{\frac{16}{4}} = \sqrt{4} = 2\)
- \(\sqrt{\frac{24}{6}} = \sqrt{4} = 2\)

Thus, the expression in option A evaluates to:
\[
2 + 2 + 2 = 6
\]

### B:
\[
(\sqrt{4^2}) + \sqrt{16} + 6^3
\]

- \(\sqrt{4^2} = \sqrt{16} = 4\)
- \(\sqrt{16} = 4\)
- \(6^3 = 216\)

Thus, the expression in option B evaluates to:
\[
4 + 4 + 216 = 224
\]

### C:
\[
(4^2 + 5^3) + \sqrt{100} + \frac{181}{6}
\]

- \(4^2 = 16\)
- \(5^3 = 125\)
- \(\sqrt{100} = 10\)
- \(\frac{181}{6} \approx 30.17\)

Thus, the expression in option C evaluates to:
\[
(16 + 125) + 10 + 30.17 = 151 + 30.17 = 181.17
\]

### D:
\[
\sqrt{\frac{8}{3}} + \sqrt{\frac{16}{3}} + \sqrt{\frac{24}{3}}
\]

- \(\sqrt{\frac{8}{3}} \approx 1.63\)
- \(\sqrt{\frac{16}{3}} \approx 2.31\)
- \(\sqrt{\frac{24}{3}} \approx 2.83\)

Thus, the expression in option D evaluates to:
\[
1.63 + 2.31 + 2.83 = 6.77
\]

### Summary of Results:
- A = 6
- B = 224
- C = 181.17
- D = 6.77

The correct value for **6** is found in option **A**.

Do you want any further details or clarifications on these steps? Here are some related questions:

1. How do you simplify square roots with fractions inside them?
2. What is the general rule for simplifying cube roots?
3. Why does \(\sqrt{4^2} = 4\) instead of 16?
4. How do you calculate fractional expressions with square roots?
5. What are the steps for evaluating complex expressions with powers and roots?

**Tip:** Always simplify the fractions first before applying square roots to make the process easier.

Evaluate the given mathematical expressions in the image and find the correct one.

Explore the solution to a set of mathematical expressions involving square roots, powers, and fractions. This problem applies fundamental arithmetic operations suitable for Grades 9-10.

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