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To simplify \( \sqrt{50} \), we need to break 50 into its prime factors and extract any perfect squares from under the square root.

1. Start by factoring 50:
   \[
   50 = 25 \times 2
   \]
   Notice that 25 is a perfect square because \( \sqrt{25} = 5 \).

2. Now, we can split the square root:
   \[
   \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2}
   \]

3. Simplifying further:
   \[
   \sqrt{50} = 5 \times \sqrt{2}
   \]

So, the simplified form of \( \sqrt{50} \) is:
\[
\boxed{5\sqrt{2}}
\]

Would you like any additional details or clarifications?

### Related Questions:
1. How would you simplify \( \sqrt{72} \)?
2. What are the steps to simplify \( \sqrt{98} \)?
3. How do you determine if a number is a perfect square?
4. What is the process for simplifying cube roots?
5. How do you simplify \( \sqrt{32} \)?

### Tip:
Always break down the number under the square root into its prime factors to check for perfect squares that can be simplified.

Simplify: Remove all perfect squares from inside the square root of \(\sqrt{50}\).

Learn how to simplify the square root of 50 by breaking it into prime factors. This solution explains how to extract perfect squares, resulting in the simplified form of \(5\sqrt{2}\). Ideal for students in Grades 7-9 looking to master simplifying radicals.

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