To solve the given problem:

We are asked to calculate $7\sqrt{6} \times \sqrt{5}$.

Solution:

1. Use the property of square roots: $\sqrt{a} \times \sqrt{b} = \sqrt{a \cdot b}$. $\sqrt{6} \times \sqrt{5} = \sqrt{6 \cdot 5} = \sqrt{30}.$

2. Multiply $7$ by $\sqrt{30}$: $7 \sqrt{30}.$

Final Answer:

$7\sqrt{30}$

This is the simplest form, as $\sqrt{30}$ cannot be simplified further (30 is not a perfect square, nor does it contain a square factor).

Would you like a detailed explanation of any step or additional examples?

Here are 5 related questions you can explore:

1. How do you simplify expressions involving surds?
2. What are the properties of square roots used in multiplication and division?
3. How do you rationalize a denominator containing a surd?
4. Can you simplify $\sqrt{45} + \sqrt{20}$?
5. How do you convert a surd into its decimal form?

Tip: Always check if the number inside the square root has square factors, as this might allow further simplification.