Express in simplest radical form.

square root of, 125, end square root

125​

To simplify \(\sqrt{125}\), we need to find the largest perfect square that divides 125. 

Here are the steps:

1. **Factor 125**:  
   \(125 = 5 \times 25 = 5 \times 5 \times 5 = 5^3\)

2. **Identify the perfect square factor**:  
   The perfect square factor of 125 is 25, which is \(5^2\).

3. **Rewrite the square root**:  
   \[
   \sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5}
   \]

4. **Simplify**:  
   \[
   \sqrt{25} = 5
   \]
   So,
   \[
   \sqrt{125} = 5\sqrt{5}
   \]

Thus, the simplest radical form of \(\sqrt{125}\) is **\(5\sqrt{5}\)**.

Would you like to explore this further or have any other questions?

Here are 5 related questions for further exploration:

1. How do you simplify \(\sqrt{200}\)?
2. What is the simplest form of \(\sqrt{50}\)?
3. Simplify \(\sqrt{180}\) in radical form.
4. Express \(\sqrt{72}\) in simplest radical form.
5. What is the square root of 48 in simplest form?

**Tip:** Always look for the largest perfect square factor when simplifying a square root.

Learn how to simplify the square root of 125 into its simplest radical form, 5√5. This detailed guide covers the process of identifying perfect square factors and applying radical simplification techniques. Suitable for Grades 7-9.

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