add 2 radical 8 + radical 28 + 2 radical 8

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. \( 4\sqrt{8} + \sqrt{28} \).