By OpenStax

Algebra and Trigonometry presents a accomplished and multi-layered exploration of algebraic rules. The textual content is acceptable for a regular introductory Algebra & Trigonometry direction, and was once built for use flexibly. The modular method and the richness of content material guarantees that the e-book meets the wishes of numerous courses. Algebra and Trigonometry publications and helps scholars with differing degrees of guidance and adventure with arithmetic. rules are awarded as truly as attainable, and development to extra advanced understandings with substantial reinforcement alongside the way in which. A wealth of examples - frequently a number of dozen in step with bankruptcy - provide exact, conceptual factors, for you to construct in scholars a powerful, cumulative origin within the fabric earlier than asking them to use what they have realized. this can be a full-color textbook.

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**Sample text**

9 5 EXTENSIONS 62. If a whole number is not a natural number, what 63. Determine whether the statement is true or false: 64. Determine whether the statement is true or false: 65. Determine whether the simplified expression is must the number be? The product of a rational and irrational number is always irrational. 66. Determine whether the simplified expression is — 5 . rational or irrational: √ −16 + 4(5) + 68. What property of real numbers would simplify the following expression: 4 + 7(x − 1)?

4 · √ 125 5 — 4 — 4 — Solution √ 3 5 — a. √ −32 = −2 because (−2)5 = −32 4 — b. First, express the product as a single radical expression. √ 4,096 = 8 because 84 = 4,096 3 — c. ________ − √ 8x Write as quotient of two radical expressions. −2x 2 _____ 5 Simplify. 6 3 — 125 √ 4 — 4 — d. 8 √ 3 − 2 √ 3 Simplify to get equal radicands. 4 — 6 √ 3 Add. Try It #10 Simplify. _______ c. 6 √ 9,000 + 7 √ 576 — 4 5 √ Using Rational Exponents Radical expressions can also be written without using the radical symbol.

B c ) 3 4 2 (3a)−2 3 39. _____ a 2 36. __ 2 3 2 1 ma 40. ( ma6) _ 3 2 −2 43. ( 9z3) y REAL-WORLD APPLICATIONS 44. To reach escape velocity, a rocket must travel at the 45. S. A 46. The average distance between Earth and the Sun is 47. 2 × 106 ft/min. Rewrite the rate in standard notation. 92,960,000 mi. Rewrite the distance using scientific notation. 2 × 106 m. Rewrite the number in standard notation. 1,099,500,000,000 bytes. Rewrite in scientific notation. 30 CHAPTER 1 Prerequisites 48.