To simplify the expression \(-3i \sqrt{-40}\), we can follow these steps: 1. Break down the square root of the negative number: \[ \sqrt{-40} = \sqrt{-1 \cdot 40} = \sqrt{-1} \cdot \sqrt{40} = i \sqrt{40} \] 2. Now we can simplify \(\sqrt{40}\): \[ \sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10} = 2\sqrt{10} \] 3. Substitute this back into the expression: \[ \sqrt{-40} = i \cdot 2\sqrt{10} = 2i\sqrt{10} \] 4. Now substitute \(2i\sqrt{10}\) into the original expression: \[ -3i \sqrt{-40} = -3i (2i \sqrt{10}) = -3 \cdot 2 \cdot i^2 \sqrt{10} \] 5. Remember that \(i^2 = -1\): \[ -3 \cdot 2 \cdot (-1) \cdot \sqrt{10} = 6\sqrt{10} \] Thus, the simplified expression is: \[ \boxed{6\sqrt{10}} \]

-3i sqrt(-40)

To simplify the expression \(-3i \sqrt{-40}\), we can follow these steps:

Break down the square root of the negative number: \[ \sqrt{-40} = \sqrt{-1 \cdot 40} = \sqrt{-1} \cdot \sqrt{40} = i \sqrt{40} \]
Now we can simplify \(\sqrt{40}\): \[ \sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10} = 2\sqrt{10} \]
Substitute this back into the expression: \[ \sqrt{-40} = i \cdot 2\sqrt{10} = 2i\sqrt{10} \]
Now substitute \(2i\sqrt{10}\) into the original expression: \[ -3i \sqrt{-40} = -3i (2i \sqrt{10}) = -3 \cdot 2 \cdot i^2 \sqrt{10} \]
Remember that \(i^2 = -1\): \[ -3 \cdot 2 \cdot (-1) \cdot \sqrt{10} = 6\sqrt{10} \]

Thus, the simplified expression is: \[ \boxed{6\sqrt{10}} \]

What's the answer

The simplified answer to the expression \(-3i \sqrt{-40}\) is:

\[ \boxed{6\sqrt{10}} \]