https://file.aiquickdraw.com/mathbot/file/1726388326031nmrvevvk.jpg

The expression shown in the image is:

\[
10\sqrt{3} + 4\sqrt{2}
\]

Since the terms involve different square roots, they cannot be simplified further by combining them. The final simplified form remains:

\[
10\sqrt{3} + 4\sqrt{2}
\]

If you are looking for a numerical approximation, we can calculate:

\[
\sqrt{3} \approx 1.732 \quad \text{and} \quad \sqrt{2} \approx 1.414
\]

Now:

\[
10\sqrt{3} \approx 10 \times 1.732 = 17.32
\]
\[
4\sqrt{2} \approx 4 \times 1.414 = 5.656
\]

Thus, the approximate sum is:

\[
17.32 + 5.656 \approx 22.976
\]

Would you like more details or a specific numerical result?

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Here are some related questions:

1. How do you simplify expressions involving square roots?
2. Can you combine terms with different square roots in any situation?
3. How do you calculate the square root of non-perfect squares?
4. What are some common approximations of irrational numbers like \( \sqrt{2} \) and \( \sqrt{3} \)?
5. What are some real-world applications of simplifying square root expressions?

**Tip:** When working with square roots, always check if you can factor out perfect squares to further simplify the expression.

Learn how to simplify the expression 10√3 + 4√2. This problem involves working with square roots and irrational numbers, with an approximate numerical solution of 22.976. Suitable for students in Grades 8-10.

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