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The problem asks for the approximation of \( 4 \sqrt{6} \) to the nearest thousandth.

Let's break it down:

1. Find the square root of 6:  
   \( \sqrt{6} \approx 2.44949 \)

2. Multiply this result by 4:  
   \( 4 \times 2.44949 \approx 9.79796 \)

To the nearest thousandth, \( 4 \sqrt{6} \approx 9.798 \).

Would you like more details on how to approximate square roots or other related topics?

Here are some related questions:
1. What is the square root of 5 to the nearest thousandth?
2. How do you calculate the square root of a non-perfect square without a calculator?
3. Can you explain the process of estimating square roots?
4. How does the square root function behave for negative numbers?
5. What are other methods to approximate square roots manually?

**Tip**: When using a calculator for square roots, ensure that you set it to display enough decimal places for higher accuracy!

Use a calculator to approximate the following square root to the nearest thousandth: 4√6 = ?

Learn how to approximate the square root of 6 and multiply by 4 to find 4√6 to the nearest thousandth. This example covers basic square root operations and is ideal for students in Grades 6-8.

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