https://file.aiquickdraw.com/mathbot/file/1726762955639t60gtxry.jpg

The problem is asking to estimate, to the nearest whole number, the value of:

\[
\sqrt{2.986^2 + 4.002^2}
\]

Let's break it down step by step:

1. Square each value:
   \[
   2.986^2 = 8.916 \quad \text{(approximately)}
   \]
   \[
   4.002^2 = 16.016 \quad \text{(approximately)}
   \]

2. Add the squared values:
   \[
   8.916 + 16.016 = 24.932
   \]

3. Take the square root of the result:
   \[
   \sqrt{24.932} \approx 4.993
   \]

4. Rounding to the nearest whole number:
   \[
   \boxed{5}
   \]

Thus, the estimated value is **5**.

Would you like a more detailed explanation of any step? Here are some related questions to expand on this:

1. What is the importance of rounding in mathematical estimations?
2. How would the answer change if the decimal places were different?
3. Why do we square the numbers before adding them in this problem?
4. How does this calculation relate to the Pythagorean theorem?
5. Can you give another example of a similar problem using different numbers?

**Tip:** When dealing with roots and powers, squaring numbers close to whole values often leads to quicker approximations.

Estimate, correct to the nearest whole number, the value of √(2.986² + 4.002²).

Learn how to estimate the value of √(2.986² + 4.002²) with a step-by-step solution. This problem covers estimation, squaring, and taking square roots, and it is suitable for students in Grades 7-10.

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