By Ron Larson
Collage Algebra with purposes for company and existence Sciences meets the call for for classes that emphasize challenge fixing, modeling, and real-world purposes for company and the lifestyles sciences. The authors supply an organization beginning in algebraic options and instructed scholars to use their knowing to correct examples and purposes they're prone to come upon in university or of their careers. extra know-how parts on hand via CL MATHSpace improve guide and inspire beginners. this system addresses the desires of scholars in any respect levels--and particularly those that can have struggled in prior algebra courses--offering an abundance of examples and routines that make stronger thoughts and make studying extra dynamic. The early advent of services in bankruptcy 1 guarantees compatibility with syllabi and gives a framework for scholar studying. non-compulsory Discovery and Exploration actions are built-in through the textual content; teachers may also choose to use graphing expertise as a device for challenge fixing and evaluation or retention.
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25 ϭ ͑Ϫ5͒2 Number Equal Factors ͑Ϫ5͒͑Ϫ5͒ Ϫ5 (square root) Ϫ64 ϭ ͑Ϫ4͒3 ͑Ϫ4͒͑Ϫ4͒͑Ϫ4͒ Ϫ4 (cube root) 81 ϭ 34 3и3 и3и3 Root 3 (fourth root) Definition of nth Root of a Number Let a and b be real numbers and let n be a positive integer. If a ϭ bn then b is an nth root of a. If n ϭ 2, the root is a square root, and if n ϭ 3, the root is a cube root. From this definition, you can see that some numbers have more than one nth root. For example, both 5 and Ϫ5 are square roots of 25. The following definition distinguishes between these two roots.
2 Find largest fourth-power factor. Rewrite. 4 Ί 3 Find fourth root. и 3x ϭ Ί͑5x͒2 и 3x b. Ί75x ϭ Ί25x 3 2 ϭ 5xΊ3x, c. x ≥ 0 Find largest square factor. Rewrite. Find root of perfect square. ͑5x͒ ϭ Խ5xԽ ϭ 5ԽxԽ 4 Ί 4 ✓CHECKPOINT 2 Simplify Ί18x5. ■ In Example 2(c), note that the absolute value symbol is included in the 4 x4 ϭ x . answer because Ί ԽԽ Example 3 Simplifying Odd Roots и3 2 и3 3 24 ϭ Ί 3 8 a. Ί ϭ Find largest cube factor. 3 3 Ί Rewrite. 3 3 ϭ 2Ί Find root of perfect cube. иa ͑2a ͒ и a 5 32a11 ϭ Ί 5 32a10 b.
SOLUTION To find the ratio, write the quotient V͞S and simplify. 7 Evaluate 5 7 7x 25x 5 when x ϭ 7. 3 Integer Exponents 23 Scientific Notation Exponents provide an efficient way of writing and computing with very large (or very small) numbers. For instance, a drop of water contains more than 33 billion billion molecules—that is, 33 followed by 18 zeros. 33,000,000,000,000,000,000 It is convenient to write such numbers in scientific notation. This notation has the form c ϫ 10 n, where 1 ≤ c < 10 and n is an integer.