Questions: Which choice is equivalent to the expression below? sqrt(-125) A. 5 i sqrt(-5) B. 5 i C. -5 i D. sqrt(125) E. 5 i sqrt(5)

Solution Steps

To solve the problem of finding an equivalent expression for \(\sqrt{-125}\), we need to express it in terms of imaginary numbers. The square root of a negative number can be expressed using the imaginary unit \(i\), where \(i = \sqrt{-1}\). Therefore, \(\sqrt{-125}\) can be rewritten as \(\sqrt{125} \cdot \sqrt{-1}\). We then simplify \(\sqrt{125}\) to \(5\sqrt{5}\), resulting in the expression \(5i\sqrt{5}\).

To find an equivalent expression for \(\sqrt{-125}\), we start by expressing it in terms of the imaginary unit \(i\), where \(i = \sqrt{-1}\). Thus, \(\sqrt{-125}\) can be rewritten as \(\sqrt{125} \cdot \sqrt{-1}\), which simplifies to \(\sqrt{125} \cdot i\).

Next, we simplify \(\sqrt{125}\). The number 125 can be factored into \(5^3\), so \(\sqrt{125} = \sqrt{5^3} = \sqrt{5^2 \cdot 5} = 5\sqrt{5}\).

Combining the results from the previous steps, we have: \[ \sqrt{-125} = 5\sqrt{5} \cdot i = 5i\sqrt{5} \]

Final Answer