Question

Express in simplest radical form.
minus, square root of, 6, end square root, plus, 6, square root of, 96, end square root
−
6
​
+6
96
​

Answer
Attempt 1 out of 5

Answer 1

To simplify the expression \(-\sqrt{6} + 6\sqrt{96}\), we begin by simplifying the term \(6\sqrt{96}\).

1. **Simplify \(\sqrt{96}\)**:
\[
\sqrt{96} = \sqrt{16 \times 6} = \sqrt{16} \times \sqrt{6} = 4\sqrt{6}
\]

2. **Multiply by 6**:
\[
6\sqrt{96} = 6 \times 4\sqrt{6} = 24\sqrt{6}
\]

3. **Combine the terms**:
The expression now becomes:
\[
-\sqrt{6} + 24\sqrt{6}
\]

Combine the like terms:
\[
(-1 + 24)\sqrt{6} = 23\sqrt{6}
\]

Therefore, the simplified form is:
\[
\boxed{23\sqrt{6}}
\]