Use the imaginary number i to rewrite the expression below as a complex number. Simplify all radicals. $$ \sqrt{-35} $$

Question

UpStudy AI · Accepted Answer

To express $$ \sqrt{-35} $$ as a complex number using the imaginary unit $$ i $$, follow these steps:

1. **Break Down the Radical:**
   $$
   \sqrt{-35} = \sqrt{35 \times (-1)}
   $$

2. **Separate the Square Roots:**
   $$
   \sqrt{35 \times (-1)} = \sqrt{35} \times \sqrt{-1}
   $$

3. **Use the Definition of $$ i $$:**
   $$
   \sqrt{-1} = i
   $$
   So,
   $$
   \sqrt{35} \times \sqrt{-1} = \sqrt{35} \times i = \sqrt{35}i
   $$

4. **Final Expression:**
   $$
   \sqrt{-35} = \sqrt{35}i
   $$

This is the simplified form of the complex number.

**Answer:** $$ \sqrt{35}\,i $$
$$ \sqrt{35}\,i $$

Use the imaginary number i to rewrite the expression below as a complex number. Simplify all radicals. \( \sqrt{-35} \)