Question

add 2 radical 8 + radical 28 + 2 radical 8

A. 5 radical 44
B. 2 radical 16 + radical 28
C. 5 radical 8
D. 4 radical 8 + radical 28

Answer 1

To simplify the expression \( 2\sqrt{8} + \sqrt{28} + 2\sqrt{8} \), we can first combine the like terms.

1. Combine the \( \sqrt{8} \) terms:
\[
2\sqrt{8} + 2\sqrt{8} = 4\sqrt{8}
\]

2. Now, we rewrite the expression:
\[
4\sqrt{8} + \sqrt{28}
\]

3. Next, we simplify \( \sqrt{8} \) and \( \sqrt{28} \):
- \( \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} \)
- \( \sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7} \)

4. Substitute these back into the expression:
\[
4\sqrt{8} = 4 \times 2\sqrt{2} = 8\sqrt{2}
\]
\[
\sqrt{28} = 2\sqrt{7}
\]
Therefore, we have:
\[
8\sqrt{2} + 2\sqrt{7}
\]

Now we can look at the options given in the original question:

- A. \( 5\sqrt{44} \)
- B. \( 2\sqrt{16} + \sqrt{28} \)
- C. \( 5\sqrt{8} \)
- D. \( 4\sqrt{8} + \sqrt{28} \)

Let's break down option D:
\[
D: 4\sqrt{8} + \sqrt{28} = 4 \times 2\sqrt{2} + 2\sqrt{7} = 8\sqrt{2} + 2\sqrt{7}
\]

This matches with \( 8\sqrt{2} + 2\sqrt{7} \).

Thus, the correct answer is:
**D. \( 4\sqrt{8} + \sqrt{28} \)**.