Write in terms of $$ i $$. Simplify your answer as much as possible, $$ \sqrt{-38} $$

Question

UpStudy AI · Accepted Answer

To express $$\sqrt{-38}$$ in terms of the imaginary unit $$i$$, follow these steps:

1. **Factor the Negative Sign**:
   $$
   \sqrt{-38} = \sqrt{38 \times (-1)}
   $$

2. **Separate the Square Root**:
   $$
   \sqrt{38 \times (-1)} = \sqrt{38} \times \sqrt{-1}
   $$

3. **Use the Definition of $$i$$**:
   $$
   \sqrt{-1} = i
   $$
   
4. **Combine the Results**:
   $$
   \sqrt{38} \times i = \sqrt{38}\,i
   $$

Since 38 factors into $$2 \times 19$$ and neither 2 nor 19 are perfect squares, the expression $$\sqrt{38}\,i$$ is already in its simplest form.

$$
\sqrt{-38} = \sqrt{38}\,i
$$
$$ \sqrt{-38} = \sqrt{38}\,i $$

Write in terms of \( i \). Simplify your answer as much as possible, \[ \sqrt{-38} \]