Questions: Express in terms of i. √(-175)

Transcript text: Express in terms of $i$. \[ \sqrt{-175} \]

Solution

Step 1: Recognize the Imaginary Unit

The square root of a negative number involves the imaginary unit $i$, where $i^2 = -1$.

Step 2: Extract the Negative Sign

By extracting the negative sign from under the square root, it converts into $i$, since $\sqrt{-1} = i$.

Step 3: Simplify the Square Root of the Positive Part

The square root of $n$ is simplified to $\sqrt{175}$, which is approximately 13.23 after rounding to 2 decimal places.

Step 4: Final Simplified Form

The final simplified form is $0 + \sqrt{175}i$ or simply $\sqrt{175}i$, which is approximately 13.23i.

The simplified form of $\sqrt{-175}$ is approximately 13.23i.

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