Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
0. Review of Algebra
Radical Expressions
0:55 minutes
Problem 5c
Textbook Question
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ___ √-36
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Square Roots
The square root of a number 'x' is a value 'y' such that y² = x. For non-negative numbers, square roots yield real numbers. However, the square root of a negative number does not yield a real number, as no real number squared results in a negative value.
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Imaginary Numbers
Imaginary numbers are defined as multiples of the imaginary unit 'i', where i is the square root of -1. This concept allows for the extension of the real number system to include solutions to equations that involve the square roots of negative numbers, such as √-36 = 6i.
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Complex Numbers
Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where 'a' is the real part and 'b' is the coefficient of the imaginary part. Understanding complex numbers is essential for evaluating expressions involving square roots of negative numbers, as they provide a complete number system.
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