Question
Write the number as a product of a real number and \( i \). Simplify all radical expressions. \( \sqrt{-12} \) \( \sqrt{-12}=\square \) (Simplify your answer. Type your answer in the form a + bi. Type an exact answer, using radicals as needed.)
Ask by Whittaker Bowen. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \sqrt{-12} = 2\sqrt{3}i \)
Solution
Calculate or simplify the expression \( \sqrt{-12} \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{-12}\)
- step1: Evaluate the power:
\(\sqrt{12}\times \sqrt{-1}\)
- step2: Evaluate the power:
\(\sqrt{12}\times i\)
- step3: Evaluate the power:
\(2\sqrt{3}\times i\)
The number \( \sqrt{-12} \) can be written as a product of a real number and \( i \) as \( 2\sqrt{3}i \).
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Simplify this solution Beyond the Answer
To write \( \sqrt{-12} \) as a product of a real number and \( i \), we first express it using \( i \): \[ \sqrt{-12} = \sqrt{12} \cdot \sqrt{-1} = \sqrt{12} \cdot i \] Next, we simplify \( \sqrt{12} \): \[ \sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \] Putting it all together, we have: \[ \sqrt{-12} = 2\sqrt{3} \cdot i \] So, the simplified form is: \[ \sqrt{-12} = 0 + 2\sqrt{3}i \]
