Question

Which of the following re-expresses the negative square root -6√-20 as a complex number in the standard form a+bi ?(1 point)
Responses

−125i−−√
negative 12 Start Root 5 i End Root

-12√5i
-12√5
-12i√5
2i√5

Answer 1

To express \(-6\sqrt{-20}\) as a complex number in the standard form \(a + bi\), we start by simplifying the expression step by step.

1. **Simplify \(-20\)**:
\[
-20 = 20 \cdot -1
\]

2. **Take the square root of \(-20\)**:
\[
\sqrt{-20} = \sqrt{20} \cdot \sqrt{-1} = \sqrt{20} \cdot i
\]
The square root of 20 can be simplified:
\[
\sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5}
\]
Thus,
\[
\sqrt{-20} = 2\sqrt{5}i
\]

3. **Multiply by \(-6\)**:
\[
-6\sqrt{-20} = -6 \cdot (2\sqrt{5}i) = -12\sqrt{5}i
\]

Now, we see that \(-6\sqrt{-20}\) is re-expressed as:
\[
-12\sqrt{5}i
\]

This matches the option:
- **-12√5i**

Thus, the correct response is **-12√5i**.