To simplify \(\sqrt{-20}\), we start by rewriting it using the property of imaginary numbers:
\[ \sqrt{-20} = \sqrt{20} \cdot \sqrt{-1} \]
We know that \(\sqrt{-1} = i\). Thus, we have:
\[ \sqrt{-20} = \sqrt{20} \cdot i \]
Next, we simplify \(\sqrt{20}\). The number 20 can be factored into 4 and 5, allowing us to break down the square root:
\[ \sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5} \]
Now, substituting back into the expression:
\[ \sqrt{-20} = 2\sqrt{5} \cdot i \]
Thus, the final simplified answer is:
\[ \sqrt{-20} = 0 + 2\sqrt{5}i \]
In the form \(a + bi\), this is:
\[ 0 + 2\sqrt{5}i \]
Therefore, the final answer is:
\[ \sqrt{-20} = 2\sqrt{5}i \]
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