Multiply these imaginary numbers and then select your answer from the choices. Make sure the answer is fully simplified. \[ \sqrt{7} i \cdot \sqrt{6} i \]

Let's solve the given problem step by step. 1. **Write the Expression:** We start with the expression \[ \sqrt{7} i \cdot \sqrt{6} i \] 2. **Multiply the Radicals:** Multiply the square roots together: \[ \sqrt{7} \cdot \sqrt{6} = \sqrt{42} \] 3. **Multiply the Imaginary Units:** Since we have two \(i\)'s, \[ i \cdot i = i^2 \] And we know that \[ i^2 = -1 \] 4. **Combine the Results:** Now, multiplying the results from the above steps, we have \[ \sqrt{42} \cdot (-1) = -\sqrt{42} \] 5. **Final Answer:** The fully simplified result is \[ -\sqrt{42} \] Thus, the answer is \(\boxed{-\sqrt{42}}\).