The expression \(\sqrt{-28}\) involves the square root of a negative number, which is not a real number. To simplify \(\sqrt{-28}\), we can use the concept of imaginary numbers.
-
First, factor out the negative sign: \[ \sqrt{-28} = \sqrt{-1 \cdot 28} \]
-
Recognize that \(\sqrt{-1} = i\), where \(i\) is the imaginary unit. Therefore: \[ \sqrt{-28} = i \sqrt{28} \]
-
Next, simplify \(\sqrt{28}\). We can factor 28 as \(4 \cdot 7\): \[ \sqrt{28} = \sqrt{4 \cdot 7} = \sqrt{4} \cdot \sqrt{7} = 2\sqrt{7} \]
-
Now, substitute back: \[ \sqrt{-28} = i \cdot 2\sqrt{7} = 2i\sqrt{7} \]
Thus, \(\sqrt{-28}\) simplified is: \[ \sqrt{-28} = 2i\sqrt{7} \]