is the square root of -121 rational or irrational

The square root of \(-121\) is neither rational nor irrational in the real number system. This is because the square root of a negative number is not a real number; instead, it is an imaginary number.

In mathematics, the square root of \(-121\) is written as \(\sqrt{-121}\), which can be expressed as \(11i\), where \(i\) is the imaginary unit defined by \(i = \sqrt{-1}\).

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Here are some related questions:

1. What are imaginary numbers?
2. How is the imaginary unit \(i\) defined?
3. What are real numbers?
4. Can imaginary numbers be rational or irrational?
5. What are complex numbers?
6. How do you simplify the square root of a negative number?
7. Are there real-world applications of imaginary numbers?
8. How do you add, subtract, multiply, and divide complex numbers?

**Tip:** Imaginary numbers extend the real number system to the complex number system, allowing for solutions to equations that have no real solutions.

Explore the nature of the square root of -121, which is neither rational nor irrational in the real number system. Learn about imaginary numbers and their representation using the imaginary unit. Suitable for high school students studying complex numbers.

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