Question

What is the sum of 711−−√+411−−√+11−−√

Answer 1

That was not the answer to this question

Answer 2

To find the sum of \( \sqrt{711} + \sqrt{411} + \sqrt{11} \), we can estimate the individual square roots.

1. **Estimating \( \sqrt{711} \)**:
\[
\sqrt{711} \approx 26.6 \quad (\text{since } 26^2 = 676 \text{ and } 27^2 = 729)
\]

2. **Estimating \( \sqrt{411} \)**:
\[
\sqrt{411} \approx 20.2 \quad (\text{since } 20^2 = 400 \text{ and } 21^2 = 441)
\]

3. **Estimating \( \sqrt{11} \)**:
\[
\sqrt{11} \approx 3.3 \quad (\text{since } 3^2 = 9 \text{ and } 4^2 = 16)
\]

Now let's add the estimates:
\[
\sqrt{711} + \sqrt{411} + \sqrt{11} \approx 26.6 + 20.2 + 3.3 = 50.1
\]

This gives an approximate sum of \( \sqrt{711} + \sqrt{411} + \sqrt{11} \approx 50.1 \).

If you need a more precise numerical value, we can calculate it using a calculator:
- \( \sqrt{711} \approx 26.681 \)
- \( \sqrt{411} \approx 20.273 \)
- \( \sqrt{11} \approx 3.317 \)

Adding these values:
\[
26.681 + 20.273 + 3.317 = 50.271
\]

Thus, the sum \( \sqrt{711} + \sqrt{411} + \sqrt{11} \approx 50.271 \).

Answer 3

I apologize for not addressing your original question correctly. Let’s focus on simplifying the expression \( \sqrt{711} + \sqrt{411} + \sqrt{11} \) instead of estimating. Here's the proper approach:

1. **Break Down the Expression**:
We’re looking for a numerical sum:

\[
\sqrt{711} + \sqrt{411} + \sqrt{11}
\]

We can calculate each square root:

- \( \sqrt{711} \)
- \( \sqrt{411} \)
- \( \sqrt{11} \)

2. **Exact Calculation**:
To get the exact values, you would typically use a calculator for precise square root values:

\( \sqrt{711} \approx 26.681 \)

\( \sqrt{411} \approx 20.273 \)

\( \sqrt{11} \approx 3.317 \)

3. **Sum Them Up**:
Now, adding them together:

\[
26.681 + 20.273 + 3.317 \approx 50.271
\]

Thus, the sum is approximately \( 50.271 \).

Please let me know if there is a specific detail or a different aspect of the question you would like to address!