By Ron Larson
This market-leading textual content maintains to supply scholars and teachers with sound, constantly established factors of the mathematical suggestions. Designed for a two-term path, the hot 8th version keeps the positive factors that experience made Algebra and Trigonometry a whole answer for either scholars and teachers: fascinating purposes, state of the art layout, and cutting edge expertise mixed with an abundance of conscientiously written routines.
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Extra info for Algebra and Trigonometry, 8th Edition
2 Exponents and Radicals 21 Simplifying Radicals An expression involving radicals is in simplest form when the following conditions are satisfied. 1. All possible factors have been removed from the radical. 2. All fractions have radical-free denominators (accomplished by a process called rationalizing the denominator). 3. The index of the radical is reduced. To simplify a radical, factor the radicand into factors whose exponents are multiples of the index. The roots of these factors are written outside the radical, and the “leftover” factors make up the new radicand.
13. The edge of each cut-out square is x inches. Find the volume of the box when x ϭ 1, x ϭ 2, and x ϭ 3. 20 − 2x 16 in. 16 − 2x x x Volume of a Box x x Solution The volume of a rectangular box is equal to the product of its length, width, and height. From the figure, the length is 20 Ϫ 2x, the width is 16 Ϫ 2x, and the height is x. So, the volume of the box is Volume ϭ ͑20 Ϫ 2x͒͑16 Ϫ 2x͒͑x͒ 20 in. ϭ ͑320 Ϫ 72x ϩ 4x 2͒͑x͒ ϭ 320x Ϫ 72x 2 ϩ 4x 3. 13 When x ϭ 1 inch, the volume of the box is Volume ϭ 320͑1͒ Ϫ 72͑1͒2 ϩ 4͑1͒3 ϭ 252 cubic inches.
5 2Ί3 b. 2 3 Ί 5 Solution a. b. 5 2Ί3 2 3 5 Ί ϭ Ί3 5 2Ί3 иΊ 3 Ί3 is rationalizing factor. ϭ 5Ί3 2͑3͒ Multiply. ϭ 5Ί3 6 Simplify. ϭ 2 3 5 Ί 3 52 Ί иΊ 3 52 3 52 is rationalizing factor. Ί ϭ 3 52 2Ί 3 Ί53 Multiply. ϭ 3 25 2Ί 5 Simplify. Now try Exercise 95. 2 Example 14 ϭ 23 Rationalizing a Denominator with Two Terms 2 2 ϭ 3 ϩ Ί7 3 ϩ Ί7 ϭ Exponents and Radicals и Multiply numerator and denominator by conjugate of denominator. 3 Ϫ Ί7 3 Ϫ Ί7 2͑3 Ϫ Ί7 ͒ 3͑3͒ ϩ 3͑ϪΊ7 ͒ ϩ Ί7͑3͒ Ϫ ͑Ί7 ͒͑Ί7 ͒ 2͑3 Ϫ Ί7 ͒ ͑3͒2 Ϫ ͑Ί7 ͒2 Use Distributive Property.