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Express \( \sqrt{-25} \) as a complex number (in terms of \( i \) ): \( \sqrt{-25}=\square \)

Ask by Gordon Olson. in the United States
Jan 23,2025

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\( \sqrt{-25} = 5i \)

Solution

Calculate or simplify the expression \( \sqrt{-25} \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{-25}\) - step1: Evaluate the power: \(\sqrt{25}\times \sqrt{-1}\) - step2: Evaluate the power: \(\sqrt{25}\times i\) - step3: Evaluate the power: \(5i\) The complex number representation of \( \sqrt{-25} \) is \( 5i \).

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To express \( \sqrt{-25} \) as a complex number, we start by recognizing that the square root of a negative number involves the imaginary unit \( i \), where \( i = \sqrt{-1} \). Therefore, we can rewrite \( \sqrt{-25} \) as follows: \[ \sqrt{-25} = \sqrt{25} \cdot \sqrt{-1} = 5i \] Thus, the expression in terms of \( i \) is: \[ \sqrt{-25} = 5i \]

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