Simplify the following
`sqrt(-9) + sqrt(-16)`

Answer

To simplify the expression \( \sqrt{-9} + \sqrt{-16} \), we can follow these steps:

### Step 1: Identify the square roots of negative numbers
We know that the square root of a negative number can be expressed in terms of the imaginary unit \( i \), where \( i = \sqrt{-1} \).

### Step 2: Rewrite the square roots
We can rewrite the given expression as:
\[ \sqrt{-9} + \sqrt{-16} = \sqrt{-1 \cdot 9} + \sqrt{-1 \cdot 16} \]

### Step 3: Factor out \( i \)
Using the property of square roots, we can factor out \( i \):
\[ \sqrt{-9} = \sqrt{-1} \cdot \sqrt{9} = i \cdot 3 = 3i \]
\[ \sqrt{-16} = \sqrt{-1} \cdot \sqrt{16} = i \cdot 4 = 4i \]

### Step 4: Combine the results
Now we can combine the two results:
\[ \sqrt{-9} + \sqrt{-16} = 3i + 4i \]

### Step 5: Simplify the expression
Adding the imaginary parts together gives:
\[ 3i + 4i = 7i \]

### Final Answer
Thus, the simplified form of \( \sqrt{-9} + \sqrt{-16} \) is:
\[ \boxed{7i} \]

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