Question

-3i sqrt(-40)

Answer 1

What's the answer

Answer 2

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

Answer 3

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

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