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
1:49 minutes
Problem 64c
Textbook Question
Textbook QuestionIn Exercises 61–82, multiply and simplify. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. __ ___ √8x ⋅ √10y
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Properties of Square Roots
The properties of square roots state that the square root of a product is equal to the product of the square roots. This means that √a ⋅ √b = √(a ⋅ b). This property is essential for simplifying expressions involving square roots, allowing us to combine terms under a single radical.
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Simplifying Radicals
Simplifying radicals involves reducing the expression under the square root to its simplest form. This includes factoring out perfect squares from the radicand. For example, √(4x) can be simplified to 2√x, making it easier to work with in calculations.
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Multiplication of Variables
When multiplying variables, it is important to combine like terms and apply the laws of exponents. For instance, when multiplying x^m by x^n, the result is x^(m+n). This concept is crucial when dealing with expressions that include variables under square roots, ensuring accurate simplification.
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