Question

Subtract. Write your answer in simplest form.
–5√6–7√150

Answer 1

To simplify the expression \(-5\sqrt{6} - 7\sqrt{150}\), we first need to simplify \(\sqrt{150}\).

1. **Simplifying \(\sqrt{150}\)**:
\[
\sqrt{150} = \sqrt{25 \times 6} = \sqrt{25} \times \sqrt{6} = 5\sqrt{6}
\]

2. **Substituting back into the expression**:
\[
-5\sqrt{6} - 7\sqrt{150} = -5\sqrt{6} - 7(5\sqrt{6}) = -5\sqrt{6} - 35\sqrt{6}
\]

3. **Combining like terms**:
\[
-5\sqrt{6} - 35\sqrt{6} = (-5 - 35)\sqrt{6} = -40\sqrt{6}
\]

Thus, the expression \(-5\sqrt{6} - 7\sqrt{150}\) simplifies to \(-40\sqrt{6}\).

The final answer is:
\[
\boxed{-40\sqrt{6}}
\]