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Let's go over the first question:

The expression given is:

\[
2\sqrt{2} - \sqrt{3} + 5\sqrt{3} - \sqrt{2}
\]

We simplify this by combining like terms:
- \(2\sqrt{2} - \sqrt{2} = \sqrt{2}\)
- \(-\sqrt{3} + 5\sqrt{3} = 4\sqrt{3}\)

So, the simplified form of the expression is:

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

This matches option **a**. So, the correct answer is **a**.

---

For the second question:

The expression is:

\[
4\sqrt{5} + 5\sqrt{6} - 9\sqrt{5} - \sqrt{2} \times 10\sqrt{3}
\]

1. Combine the terms with \( \sqrt{5} \):
   \[
   4\sqrt{5} - 9\sqrt{5} = -5\sqrt{5}
   \]

2. The \( 5\sqrt{6} \) stays as it is.

3. Simplify \( \sqrt{2} \times 10\sqrt{3} \):
   \[
   \sqrt{2} \times 10\sqrt{3} = 10\sqrt{6}
   \]

So, the expression becomes:

\[
-5\sqrt{5} + 5\sqrt{6} - 10\sqrt{6}
\]

Finally, combine the \( \sqrt{6} \) terms:

\[
5\sqrt{6} - 10\sqrt{6} = -5\sqrt{6}
\]

Thus, the simplified form is:

\[
-5\sqrt{5} - 5\sqrt{6}
\]

This matches option **a**.

---

Would you like further details or have any questions about these solutions?

Here are 5 related questions for more practice:
1. Simplify \( 3\sqrt{7} - 2\sqrt{7} + 5\sqrt{7} \).
2. What is \( \sqrt{8} + \sqrt{18} \) in its simplest form?
3. Simplify \( 4\sqrt{3} - 7\sqrt{3} + 6\sqrt{3} \).
4. Find the value of \( \sqrt{50} + \sqrt{2} \).
5. Simplify \( 2\sqrt{12} - 3\sqrt{3} + 4\sqrt{27} \).

**Tip:** When simplifying square roots, always group terms with the same radicals first before combining them.

Bentuk sederhana dari operasi 2√2 - √3 + 5√3 - √2 adalah...

Learn how to simplify the radical expression 2√2 - √3 + 5√3 - √2 by combining like terms of square roots. This problem involves properties of radicals and algebraic simplifications. Suitable for students in Grades 9-10.

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