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

To re-express the negative square root \(-6 - 20\sqrt{}\) as a complex number in standard form \(a + bi\), we first need to evaluate the expression inside the square root.

1. We start with the expression: \[ -6 - 20 \] Here, we can combine these terms: \[ -6 - 20 = -26 \]

2. Now, we need to take the square root of \(-26\): \[ \sqrt{-26} = \sqrt{26} \cdot \sqrt{-1} = \sqrt{26} i \]

3. Since we want the negative square root: \[ -\sqrt{-26} = -\sqrt{26} i \]

4. We should write \(\sqrt{26}\) in terms of its prime factors. The prime factorization of 26 is \(2 \cdot 13\), but we can express this as: \[ \sqrt{26} = \sqrt{2 \cdot 13} = \sqrt{2} \cdot \sqrt{13} \]

However, for practical purposes in expressing as a complex number, we will leave it as \(\sqrt{26}\).

5. Finally, we can express the complex number in standard form: \[ -\sqrt{26} i \]

Now we compare this with the options provided.

The correct representation of \(-\sqrt{26} i\) in the options given is: \[ -\sqrt{12} (\sqrt{5}) i = -12 \sqrt{5} i \] However, there might be some mix-up in the numbers in the options provided since \(-\sqrt{26} i\) doesn't match the given options perfectly.

Given this reasoning, find which expression fits. The likely intended option seems to be: \[ -\sqrt{12 (\sqrt{5})} i = -12 \sqrt{5} i \] So, the most reasonable fit from the options is: \(-12i \sqrt{5}\).

Check with your exam or task to ensure this reasoning aligns correctly, as none of the options given might perfectly match \(-\sqrt{26} i\).