The radical form of \( 500 \) can be simplified by factoring out perfect squares. Let's go through the steps:

1. Break \( 500 \) into factors:
   \[
   500 = 100 \times 5
   \]

2. Since \( 100 \) is a perfect square (\( 100 = 10^2 \)), we can simplify the square root of 100:
   \[
   \sqrt{500} = \sqrt{100 \times 5} = \sqrt{100} \times \sqrt{5} = 10\sqrt{5}
   \]

Thus, the simplified form of \( \sqrt{500} \) is:
\[
\boxed{10\sqrt{5}}
\]

Would you like further details or have any questions?

Here are 5 related questions you might find helpful:
1. How do you simplify the square root of a non-perfect square?
2. What are perfect squares, and how are they useful in simplifying radicals?
3. Can all square roots be simplified?
4. How would you simplify \( \sqrt{72} \)?
5. What is the decimal approximation of \( 10\sqrt{5} \)?

**Tip**: When simplifying radicals, always look for the largest perfect square factor to simplify more easily!

Discover how to simplify the square root of 500 by factoring perfect squares. This detailed step-by-step solution covers essential concepts like radicals, simplification, and the use of perfect squares. Perfect for students in Grades 7-9 looking to master radical expressions.

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