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To simplify \( \sqrt{125} \) to the form \( a\sqrt{b} \), we follow these steps:

### Step 1: Prime factorization of 125
125 can be written as:
\[
125 = 5 \times 5 \times 5 = 5^3
\]

### Step 2: Simplify the square root
\[
\sqrt{125} = \sqrt{5^3} = \sqrt{5^2 \times 5} = 5\sqrt{5}
\]

### Final Answer:
\[
\sqrt{125} = 5\sqrt{5}
\]

Would you like further clarification or more details?

Here are 5 related questions to expand your understanding:
1. How do you simplify other square roots like \( \sqrt{75} \)?
2. Can you express \( \sqrt{500} \) in the form \( a\sqrt{b} \)?
3. What is the general method to simplify any square root?
4. How would you handle a cube root, such as \( \sqrt[3]{125} \)?
5. How does the prime factorization method help in simplifying square roots?

**Tip:** Always look for perfect squares within the number under the square root to simplify more easily.

Simplify \( \sqrt{125} \) to the form \( a\sqrt{b} \).

Learn how to simplify the square root of 125 to the form a√b by using prime factorization. This math problem demonstrates simplifying square roots with a step-by-step solution, suitable for students in Grades 7-9.

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