Question
Write in terms of \( i \), Simplify your answer as much as possible \[ \sqrt{-100} \]
Ask by Klein Hart. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \sqrt{-100} = 10i \)
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The Deep Dive
To write \( \sqrt{-100} \) in terms of \( i \), we first recognize that the square root of a negative number can be expressed using the imaginary unit \( i \), where \( i = \sqrt{-1} \). We can rewrite \( \sqrt{-100} \) as: \[ \sqrt{-100} = \sqrt{100} \cdot \sqrt{-1} = 10i \] So, the simplified form of \( \sqrt{-100} \) is \( 10i \).
