Wagner Young
01/07/2024 · Primary School
Express the radical using the imaginary unit, \( i \). Express your answer in simplified form. \( \pm \sqrt{-55}= \pm \square \)
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Tutor-Verified Answer
Step-by-step Solution
To express the radical \( \pm \sqrt{-55} \) using the imaginary unit \( i \), we start by recognizing that the square root of a negative number can be expressed in terms of \( i \).
We can rewrite \( \sqrt{-55} \) as follows:
\[
\sqrt{-55} = \sqrt{55} \cdot \sqrt{-1}
\]
Since \( \sqrt{-1} = i \), we have:
\[
\sqrt{-55} = \sqrt{55} \cdot i
\]
Thus, we can express \( \pm \sqrt{-55} \) as:
\[
\pm \sqrt{-55} = \pm \sqrt{55} \cdot i
\]
Therefore, the simplified form is:
\[
\pm \sqrt{-55} = \pm \sqrt{55} i
\]
So, the answer is:
\[
\pm \sqrt{-55} = \pm \sqrt{55} i
\]
Quick Answer
\[
\pm \sqrt{-55} = \pm \sqrt{55} i
\]
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