Question
Calculate the value of this expression and then select your answer from the choices. Make sure your answer is fully simplified. \[ \sqrt{3} i \cdot \sqrt{4} i \]
Ask by Romero Thornton. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The value of the expression is \(-2\sqrt{3}\).
Solution

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Beyond the Answer
To evaluate the expression \(\sqrt{3} i \cdot \sqrt{4} i\), we first simplify the square roots. We know that \(\sqrt{4} = 2\). Therefore, we have: \[ \sqrt{3} i \cdot \sqrt{4} i = \sqrt{3} i \cdot 2 i \] This can be rearranged and simplified as follows: \[ = 2 \cdot \sqrt{3} \cdot i^2 \] Since \(i^2 = -1\), we substitute that in: \[ = 2 \cdot \sqrt{3} \cdot (-1) = -2\sqrt{3} \] So the final answer, fully simplified, is: \(-2\sqrt{3}\)