Question

add 2 radical 8 + radical 28 + 2 radical 8

Answer 1

To simplify the expression \( 2\sqrt{8} + \sqrt{28} + 2\sqrt{8} \), let's start by combining like terms.

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

2. **Now let's rewrite \( \sqrt{28} \):**
\[
\sqrt{28} = \sqrt{4 \cdot 7} = \sqrt{4} \cdot \sqrt{7} = 2\sqrt{7}
\]

3. **Now substitute back into the expression:**
\[
4\sqrt{8} + \sqrt{28} = 4\sqrt{8} + 2\sqrt{7}
\]

4. **Rewrite \( \sqrt{8} \):**
\[
\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}
\]
So,
\[
4\sqrt{8} = 4(2\sqrt{2}) = 8\sqrt{2}
\]

5. **Finally, combine everything:**
\[
8\sqrt{2} + 2\sqrt{7}
\]

Thus, the simplified expression is:
\[
8\sqrt{2} + 2\sqrt{7}
\]