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
1. Equations & Inequalities
Linear Equations
2:36 minutes
Problem 74b
Textbook Question
Textbook QuestionExercises 73–75 will help you prepare for the material covered in the next section. Simplify: √18 - √8
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Radical Expressions
Radical expressions involve roots, such as square roots, cube roots, etc. In this context, we are dealing with square roots, which represent a number that, when multiplied by itself, gives the original number. Understanding how to simplify these expressions is crucial for solving problems involving radicals.
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Simplifying Square Roots
To simplify square roots, we look for perfect squares within the radicand (the number under the root). For example, √18 can be simplified to √(9*2) = 3√2, and √8 can be simplified to √(4*2) = 2√2. This process helps in reducing the expression to its simplest form.
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Imaginary Roots with the Square Root Property
Combining Like Terms
Combining like terms is a fundamental algebraic skill that involves adding or subtracting terms that have the same variable or radical part. In the expression √18 - √8, after simplification, we combine the resulting terms (if they share the same radical) to arrive at a final simplified expression.
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