The given expression is \( 3\sqrt{7} \times \sqrt{8} + 5\sqrt{14} \).

Let's break it down step by step:

1. **Multiply the square roots**: 
   - \( \sqrt{7} \times \sqrt{8} = \sqrt{7 \times 8} = \sqrt{56} \)
   - The expression now becomes \( 3\sqrt{56} + 5\sqrt{14} \).

2. **Simplify \( \sqrt{56} \)**:
   - \( \sqrt{56} = \sqrt{4 \times 14} = \sqrt{4} \times \sqrt{14} = 2\sqrt{14} \)
   - The expression becomes \( 3 \times 2\sqrt{14} + 5\sqrt{14} = 6\sqrt{14} + 5\sqrt{14} \).

3. **Combine like terms**:
   - \( 6\sqrt{14} + 5\sqrt{14} = (6 + 5)\sqrt{14} = 11\sqrt{14} \).

So, the simplified expression is \( 11\sqrt{14} \).

Would you like more details or have any questions about this solution?

Here are 5 related questions:
1. How do you simplify expressions involving square roots?
2. What are the properties of square roots that allow multiplication like \( \sqrt{a} \times \sqrt{b} \)?
3. How would you simplify an expression like \( 4\sqrt{18} + 3\sqrt{2} \)?
4. Can you explain how to combine like terms involving square roots?
5. What is the general process for simplifying radical expressions?

**Tip:** Always look for perfect square factors when simplifying square roots.

This guide explains how to simplify the radical expression 3√7 x √8 + 5√14, covering the multiplication and simplification of square roots, and combining like terms. Suitable for students in Grades 9-10.

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