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!

Learn how to simplify 3√50 to 15√2 using prime factorization. This step-by-step explanation covers simplifying square roots, breaking down radicals, and multiplying whole numbers with square roots. Perfect for students in Grades 6-8.

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