Simplify:
`sqrt(-20) + sqrt(-12)`

Answer

To simplify the expression \( \sqrt{-20} + \sqrt{-12} \), we can follow these steps:

### Step 1: Rewrite the square roots using imaginary unit \( i \)
We know that \( \sqrt{-1} = i \). Therefore, we can rewrite the square roots of negative numbers as follows:
\[ \sqrt{-20} = \sqrt{20} \cdot \sqrt{-1} = \sqrt{20} \cdot i \]
\[ \sqrt{-12} = \sqrt{12} \cdot \sqrt{-1} = \sqrt{12} \cdot i \]

### Step 2: Simplify the square roots
Next, we simplify \( \sqrt{20} \) and \( \sqrt{12} \):
\[ \sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5} \]
\[ \sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \]

### Step 3: Substitute back into the expression
Now we can substitute these simplified forms back into the expression:
\[ \sqrt{-20} + \sqrt{-12} = 2\sqrt{5} \cdot i + 2\sqrt{3} \cdot i \]

### Step 4: Factor out the common term
We can factor out the common term \( 2i \):
\[ 2\sqrt{5} \cdot i + 2\sqrt{3} \cdot i = 2i(\sqrt{5} + \sqrt{3}) \]

### Final Answer
Thus, the simplified form of \( \sqrt{-20} + \sqrt{-12} \) is:
\[ \boxed{2i(\sqrt{5} + \sqrt{3})} \]