Questions: Simplify the following radical. [ sqrt-75 ]

Solution Steps

We start with the expression \( \sqrt{-75} \).

Recognizing that \( \sqrt{-1} = i \), we can rewrite the expression as: \[ \sqrt{-75} = \sqrt{75} \cdot \sqrt{-1} = \sqrt{75} \cdot i \]

Next, we simplify \( \sqrt{75} \). We can factor \( 75 \) as \( 25 \times 3 \): \[ \sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \cdot \sqrt{3} = 5\sqrt{3} \]

Substituting back into our expression, we have: \[ \sqrt{-75} = 5\sqrt{3} \cdot i \]

Final Answer