Write in terms of $$ i $$. Simplify your answer as much as possible. $$ \sqrt{-26} $$

Question

UpStudy AI · Accepted Answer

To simplify $$\sqrt{-26}$$ in terms of the imaginary unit $$i$$, follow these steps:

1. **Understand the Imaginary Unit:**  
   The imaginary unit $$i$$ is defined as $$i = \sqrt{-1}$$.

2. **Express the Square Root of a Negative Number:**  
   For any positive real number $$k$$, $$\sqrt{-k} = i\sqrt{k}$$.

3. **Apply to $$\sqrt{-26}$$:**  
   $$
   \sqrt{-26} = i\sqrt{26}
   $$

So, the simplified form of $$\sqrt{-26}$$ is:

$$
\sqrt{-26} = i\sqrt{26}
$$
$$\sqrt{-26} = i\sqrt{26}$$

Write in terms of \( i \). Simplify your answer as much as possible. \[ \sqrt{-26} \]