e the imaginary number \( i \) to rewrite the expression below as a complex number. Simplify radicals. \( -\sqrt{-51} \)

To rewrite the expression \( -\sqrt{-51} \) as a complex number, we can use the imaginary unit \( i \), where \( i = \sqrt{-1} \). 1. **Express the Square Root of a Negative Number:** \[ \sqrt{-51} = \sqrt{51 \cdot (-1)} = \sqrt{51} \cdot \sqrt{-1} = \sqrt{51} \cdot i \] 2. **Apply the Negative Sign:** \[ -\sqrt{-51} = -\sqrt{51} \cdot i \] 3. **Simplify the Radical (if possible):** Check if \( 51 \) has any perfect square factors: \[ 51 = 3 \times 17 \] Since neither \( 3 \) nor \( 17 \) are perfect squares, \( \sqrt{51} \) cannot be simplified further. 4. **Final Answer:** \[ -\sqrt{51}\,i \] **Answer:** \( -\,\sqrt{51}\;i \)