The expression $3\sqrt{50}$ can be simplified as follows:

1. First, simplify $\sqrt{50}$. We can break it down into prime factors: $\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$

2. Now, substitute $\sqrt{50}$ with $5\sqrt{2}$: $3\sqrt{50} = 3 \times 5\sqrt{2} = 15\sqrt{2}$

So, the simplified form of $3\sqrt{50}$ is $15\sqrt{2}$.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you simplify square roots with non-perfect square factors?
2. Can you break down the square root of any number into simpler terms?
3. How would $5\sqrt{18}$ be simplified?
4. What are the rules for multiplying a whole number by a square root?
5. How do you add or subtract numbers with square roots, like $3\sqrt{50} + 2\sqrt{18}$?

Tip: Always look for perfect square factors when simplifying square roots!