Question

Add. Write your answer in simplest form.
8√2 + 6√72

Answer 1

To simplify the expression \(8\sqrt{2} + 6\sqrt{72}\), we first need to simplify \(6\sqrt{72}\).

1. **Simplifying \(\sqrt{72}\)**:
\[
\sqrt{72} = \sqrt{36 \cdot 2} = \sqrt{36} \cdot \sqrt{2} = 6\sqrt{2}
\]
Therefore, we can express \(6\sqrt{72}\) as:
\[
6\sqrt{72} = 6 \cdot 6\sqrt{2} = 36\sqrt{2}
\]

2. **Now substitute back into the original expression**:
\[
8\sqrt{2} + 6\sqrt{72} = 8\sqrt{2} + 36\sqrt{2}
\]

3. **Combine the like terms**:
\[
(8 + 36)\sqrt{2} = 44\sqrt{2}
\]

Thus, the simplest form of \(8\sqrt{2} + 6\sqrt{72}\) is:
\[
\boxed{44\sqrt{2}}
\]