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

College Algebra

0. Review of Algebra

Radical Expressions

1:19 minutes

Problem 119a

Textbook Question

Perform the indicated operations. Assume all variables represent positive real numbers. (√2 + 3) (√2 - 3)

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Difference of Squares

The difference of squares is a fundamental algebraic identity that states that the product of two binomials, where one is the sum and the other is the difference of the same two terms, can be expressed as the difference of their squares. Specifically, (a + b)(a - b) = a² - b². In this case, applying this identity to (√2 + 3)(√2 - 3) simplifies the expression significantly.

Radicals

Radicals are expressions that involve roots, such as square roots, cube roots, etc. In this problem, √2 is a radical expression representing the positive square root of 2. Understanding how to manipulate radicals, including simplifying them and performing operations with them, is essential for solving problems that involve square roots.

Algebraic Operations

Algebraic operations include addition, subtraction, multiplication, and division of algebraic expressions. In this question, performing the indicated operations requires knowledge of how to multiply binomials and apply the distributive property. Mastery of these operations is crucial for simplifying expressions and solving algebraic equations effectively.