Question

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

Answer 1

whats the answer?

Answer 2

the answer is not 50.26

Answer 3

To find the sum \( \sqrt{711} + \sqrt{411} + \sqrt{11} \), we can evaluate each square root separately, then sum them up.

1. **Calculating \( \sqrt{711} \)**:
- To approximate \( \sqrt{711} \), we can find two perfect squares that are close to 711. We know \( 26^2 = 676 \) and \( 27^2 = 729 \). This implies that \( 26 < \sqrt{711} < 27 \).
- More precisely, we can use a calculator or approximation technique to find \( \sqrt{711} \approx 26.6 \).

2. **Calculating \( \sqrt{411} \)**:
- For \( \sqrt{411} \), we see that \( 20^2 = 400 \) and \( 21^2 = 441 \), so \( 20 < \sqrt{411} < 21 \).
- Using a calculator gives \( \sqrt{411} \approx 20.273 \).

3. **Calculating \( \sqrt{11} \)**:
- We know \( 3^2 = 9 \) and \( 4^2 = 16 \), which means \( 3 < \sqrt{11} < 4 \).
- Using a calculator gives \( \sqrt{11} \approx 3.317 \).

Now, we sum these approximate values:

\[
\sqrt{711} + \sqrt{411} + \sqrt{11} \approx 26.6 + 20.273 + 3.317
\]

Calculating the sum:

\[
26.6 + 20.273 = 46.873
\]

Now adding \( 3.317 \):

\[
46.873 + 3.317 \approx 50.19
\]

Thus, the sum \( \sqrt{711} + \sqrt{411} + \sqrt{11} \approx 50.19 \).

For an exact final answer, the most suitable approximation is:

\[
\sqrt{711} + \sqrt{411} + \sqrt{11} \approx 50.19
\]

This is a rounded approximation. The exact sum cannot be simplified further without numerical calculations.

Answer 4

The sum of the square roots \( \sqrt{711} + \sqrt{411} + \sqrt{11} \) can be approximated as follows:

1. \( \sqrt{711} \approx 26.66 \)
2. \( \sqrt{411} \approx 20.273 \)
3. \( \sqrt{11} \approx 3.317 \)

Adding these values together:

\[
\sqrt{711} + \sqrt{411} + \sqrt{11} \approx 26.66 + 20.273 + 3.317 \approx 50.25
\]

So, the approximate answer to the sum \( \sqrt{711} + \sqrt{411} + \sqrt{11} \) is approximately \( 50.25 \).

If you need a more exact numeric value, you can use a calculator to find:

\[
\sqrt{711} \approx 26.67, \quad \sqrt{411} \approx 20.273 \quad \text{and} \quad \sqrt{11} \approx 3.317
\]

And adding them:

\[
26.67 + 20.273 + 3.317 \approx 50.26
\]

Thus, the exact numerical answer to the sum is approximately \( 50.26 \).

Answer 5

Let's calculate \( \sqrt{711} + \sqrt{411} + \sqrt{11} \) more accurately step by step.

First, let's find the approximate values of each square root:

1. **Calculating \( \sqrt{711} \)**:
\[
\sqrt{711} \approx 26.67
\]

2. **Calculating \( \sqrt{411} \)**:
\[
\sqrt{411} \approx 20.273
\]

3. **Calculating \( \sqrt{11} \)**:
\[
\sqrt{11} \approx 3.317
\]

Now, we will sum these values:

\[
\sqrt{711} + \sqrt{411} + \sqrt{11} \approx 26.67 + 20.273 + 3.317
\]

Calculating that step-by-step:

1. First add \( 26.67 + 20.273 \):
\[
= 46.943
\]

2. Then add \( 3.317 \):
\[
46.943 + 3.317 \approx 50.26
\]

However, if you believe the answer is incorrect, I apologize if the computations were not aligned with expectations. Let's find the exact numerical values using a calculator:

1. **Using a calculator**:
- \( \sqrt{711} \approx 26.683 \)
- \( \sqrt{411} \approx 20.273 \)
- \( \sqrt{11} \approx 3.317 \)

Now summing these precisely:

\[
26.683 + 20.273 + 3.317 \approx 50.273
\]

So, if we sum them precisely:

\[
\sqrt{711} + \sqrt{411} + \sqrt{11} \approx 50.273
\]

If your computed answer differs significantly, could you please clarify what your expected answer is? Or if there is any specific method or simplification you're looking for? Thank you for your patience!