Use the imaginary number $$ i $$ to rewrite the expression below as a complex number. Simplify all radicals. $$ \sqrt{-12} $$

Question

UpStudy AI · Accepted Answer

To rewrite the expression $$\sqrt{-12}$$ as a complex number using the imaginary unit $$i$$, follow these steps:

1. **Separate the negative sign:**
   $$
   \sqrt{-12} = \sqrt{12} \times \sqrt{-1}
   $$

2. **Express $$\sqrt{-1}$$ as $$i$$:**
   $$
   \sqrt{-12} = \sqrt{12} \times i
   $$

3. **Simplify $$\sqrt{12}$$:**
   $$
   \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
   $$

4. **Combine the results:**
   $$
   \sqrt{-12} = 2\sqrt{3} \, i
   $$

So, the expression $$\sqrt{-12}$$ rewritten as a complex number is:

$$
2\,\sqrt{3}\,i
$$
The expression $$\sqrt{-12}$$ as a complex number is $$2\sqrt{3}i$$.

Use the imaginary number \( i \) to rewrite the expression below as a complex number. Simplify all radicals. \[ \sqrt{-12} \]