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Let's solve the problem in question 24. It asks for the result of \( 3\sqrt{15} \times 5\sqrt{3} \).

### Step-by-step solution:

1. **Multiply the coefficients**:
   - The coefficients outside the square roots are 3 and 5.
   - \( 3 \times 5 = 15 \).

2. **Multiply the square roots**:
   - Inside the square roots, we have \( \sqrt{15} \times \sqrt{3} \).
   - Recall that \( \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \).
   - So, \( \sqrt{15} \times \sqrt{3} = \sqrt{45} \).

3. **Simplify \( \sqrt{45} \)**:
   - \( 45 = 9 \times 5 \), and since \( \sqrt{9} = 3 \), we can simplify:
   - \( \sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5} \).

4. **Final multiplication**:
   - Now we multiply the 15 from the first step with the simplified square root:
   - \( 15 \times 3\sqrt{5} = 45\sqrt{5} \).

So, the result is \( 45\sqrt{5} \).

### The correct answer is option **B**.

Would you like more details or explanations on any step?

Here are some related questions to expand on this:

1. How do you multiply two square roots with different numbers?
2. How do you simplify square roots involving perfect squares?
3. Can you explain how to handle coefficients when multiplying square roots?
4. How does multiplying radicals differ from adding them?
5. What is the general rule for multiplying expressions with square roots?

**Tip:** Always look for ways to simplify square roots, especially when perfect square factors are present.

This math problem demonstrates how to multiply and simplify radicals. Learn how to find the result of 3√15 × 5√3 using key algebraic concepts and formulas. Suitable for students in Grades 8-10.

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