What is the square root of negative 100?
Understand the Problem
The question is asking for the square root of a negative number, specifically -100. In mathematics, the square root of a negative number involves the concept of imaginary numbers. The square root of -100 can be expressed as 10i, where 'i' represents the imaginary unit.
Answer
$10i$
Answer for screen readers
The square root of -100 is $10i$.
Steps to Solve
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Identify the negative number We need to find the square root of the negative number $-100$.
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Use the properties of square roots We know that the square root of a negative number can be expressed in terms of the imaginary unit $i$, where $i^2 = -1$. Therefore, we can rewrite the square root as follows:
$$ \sqrt{-100} = \sqrt{100} \cdot \sqrt{-1} $$
- Calculate the square root of 100 Now we find the square root of the positive part:
$$ \sqrt{100} = 10 $$
- Combine the results Now we can combine our findings:
$$ \sqrt{-100} = 10 \cdot i $$
Thus, the square root of -100 is $10i$.
The square root of -100 is $10i$.
More Information
In mathematics, imaginary numbers extend our number system, allowing us to work with square roots of negative numbers. The notation $i$ stands for the imaginary unit and is defined as $i = \sqrt{-1}$. This concept is widely used in fields like electrical engineering and complex number theory.
Tips
- Confusing the square root of a negative number with a real number. Remember, the square root of a negative number is not a real number, but an imaginary one. Always include the $i$ when dealing with square roots of negatives.
