To solve $3 \sqrt{5} \times \sqrt{10}$, we can follow these steps:

1. First, combine the square roots using the property of radicals: $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$.

   $3 \sqrt{5} \times \sqrt{10} = 3 \times \sqrt{5 \times 10}$

2. Calculate the product inside the square root:

   $5 \times 10 = 50$

   So, we have:

   $3 \times \sqrt{50}$

3. Simplify $\sqrt{50}$ by finding its prime factors:

   $\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \sqrt{2}$

4. Substitute back:

   $3 \times 5 \sqrt{2} = 15 \sqrt{2}$

So, the answer is:

$15 \sqrt{2}$

Would you like further explanation or have any questions?

Here are five related questions to consider:

1. How would you solve $4 \sqrt{3} \times \sqrt{12}$?
2. What is the general approach for simplifying expressions with square roots?
3. Can you multiply two square roots directly without combining them under a single root?
4. What is the result of $\sqrt{18} \times \sqrt{2}$?
5. How would you simplify $5 \sqrt{7} \times \sqrt{14}$?

Tip: When simplifying square roots, factor them to see if any perfect squares can be pulled out for easier simplification.