Question

What is the sum of the following expression? 2108−−−√+48−−√+527−−√ (1 point)

Answer 1

To calculate the sum of the expression \( \sqrt{2108} + \sqrt{48} + \sqrt{527} \), we will evaluate each square root individually.

1. **Calculating \( \sqrt{2108} \)**:
- First, note that \( 2108 = 4 \times 527 \).
- Therefore, \( \sqrt{2108} = \sqrt{4 \times 527} = \sqrt{4} \times \sqrt{527} = 2\sqrt{527} \).

2. **Calculating \( \sqrt{48} \)**:
- We can simplify \( \sqrt{48} \) since \( 48 = 16 \times 3 \).
- Thus, \( \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} \).

3. **Calculating \( \sqrt{527} \)**:
- The number 527 does not have a perfect square factor, so we will leave it as \( \sqrt{527} \).

Now we can rewrite the expression:

\[
\sqrt{2108} + \sqrt{48} + \sqrt{527} = 2\sqrt{527} + 4\sqrt{3} + \sqrt{527}
\]

Combining like terms:

\[
(2\sqrt{527} + \sqrt{527}) + 4\sqrt{3} = 3\sqrt{527} + 4\sqrt{3}
\]

Thus, the final result is:

\[
\sqrt{2108} + \sqrt{48} + \sqrt{527} = 3\sqrt{527} + 4\sqrt{3}
\]

This does not simplify to a numeric value without calculating the values of \( \sqrt{527} \) and \( \sqrt{3} \).

To get the approximate numeric value, we can calculate:

- \( \sqrt{527} \approx 22.9 \)
- \( \sqrt{3} \approx 1.732 \)

Substituting:

\[
3 \cdot 22.9 + 4 \cdot 1.732 \approx 68.7 + 6.928 \approx 75.628
\]

Therefore, the sum \( \sqrt{2108} + \sqrt{48} + \sqrt{527} \) is approximately \( 75.63 \).

If needed, you can present the answer as **\( 3\sqrt{527} + 4\sqrt{3} \)** or approximately **75.63**.