Simplify : `3sqrt(-16)-2sqrt(-9)+4sqrt(-36)`

Explanation

To simplify the expression \( 3\sqrt{-16} - 2\sqrt{-9} + 4\sqrt{-36} \), we will follow these steps:

### Step 1: Rewrite the square roots of negative numbers
We know that \( \sqrt{-a} = \sqrt{a} \cdot i \), where \( i = \sqrt{-1} \). Therefore, we can rewrite each term in the expression:

\[ 3\sqrt{-16} = 3\sqrt{16} \cdot i = 3 \cdot 4 \cdot i = 12i \]

\[ -2\sqrt{-9} = -2\sqrt{9} \cdot i = -2 \cdot 3 \cdot i = -6i \]

\[ 4\sqrt{-36} = 4\sqrt{36} \cdot i = 4 \cdot 6 \cdot i = 24i \]

### Step 2: Substitute back into the expression
Now we can substitute these results back into the original expression:

\[ 12i - 6i + 24i \]

### Step 3: Combine like terms
Now, we combine the coefficients of \( i \):

\[ (12 - 6 + 24)i = (6 + 24)i = 30i \]

### Final Answer
Thus, the simplified form of the expression \( 3\sqrt{-16} - 2\sqrt{-9} + 4\sqrt{-36} \) is:

\[ \boxed{30i} \]

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