Questions: Express in terms of i. √(-125) √(-125)= (Simplify your answer. Type your answer in the form a + bi.)

Solution Steps

To express \(\sqrt{-125}\) in terms of \(i\), we need to recognize that the square root of a negative number can be expressed using the imaginary unit \(i\), where \(i = \sqrt{-1}\). First, we separate the negative sign and the positive part of the number: \(\sqrt{-125} = \sqrt{-1 \times 125}\). This can be rewritten as \(\sqrt{-1} \times \sqrt{125}\), which simplifies to \(i \times \sqrt{125}\). Finally, we simplify \(\sqrt{125}\) to its simplest radical form.

We start with the expression \(\sqrt{-125}\). To simplify this, we recognize that it involves a negative number under the square root.

We can express \(\sqrt{-125}\) as: \[ \sqrt{-125} = \sqrt{-1 \times 125} = \sqrt{-1} \times \sqrt{125} \] Here, we identify \(\sqrt{-1}\) as \(i\), the imaginary unit.

Next, we simplify \(\sqrt{125}\): \[ \sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5} \] Thus, we can rewrite our expression as: \[ \sqrt{-125} = i \times 5\sqrt{5} \]

Final Answer