By Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger
Those authors have created a booklet to truly aid scholars visualize arithmetic for greater comprehension. by way of developing algebraic visible side-by-sides to resolve numerous difficulties within the examples, the authors exhibit scholars the connection of the algebraic answer with the visible, frequently graphical, answer. additionally, the authors have additional various new instruments to aid scholars greater use the booklet for optimum effectiveness not to in basic terms cross the direction, yet actually comprehend the material.
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Extra info for Algebra and Trigonometry (3rd Edition) (Beecher/Penna/Bittinger Series)
6 39 • Radical Notation and Rational Exponents nth Root A number c is said to be an nth root of a if c n a. The symbol ͙a denotes the nonnegative square root of a, and the symn 3 bol ͙ a denotes the real-number cube root of a. The symbol ͙ a denotes n the nth root of a, that is, a number whose nth power is a. The symbol ͙ is called a radical, and the expression under the radical is called the radicand. The number n (which is omitted when it is 2) is called the index. Examples of roots for n 3, 4, and 2, respectively, are 3 4 ͙ 125, ͙ 16, and ͙3600.
QXP 34 Chapter R 12/2/04 2:43 PM Page 34 • Basic Concepts of Algebra To find the least common denominator of rational expressions, factor each denominator and form the product that uses each factor the greatest number of times it occurs in any factorization. EXAMPLE 5 Add or subtract and simplify each of the following. x Ϫ 4x ϩ 4 xϩ4 ϩ 2x 2 Ϫ 3x ϩ 1 2x Ϫ 2 x 5 Ϫ 2 b) 2 x ϩ 11x ϩ 30 x ϩ 9x ϩ 20 2 a) Solution x 2 Ϫ 4x ϩ 4 xϩ4 ϩ a) 2 2x Ϫ 3x ϩ 1 2x Ϫ 2 x 2 Ϫ 4x ϩ 4 xϩ4 Factoring the denominators ϩ ͑2x Ϫ 1͒͑x Ϫ 1͒ 2͑x Ϫ 1͒ The LCD is ͑2x Ϫ 1͒ ͑x Ϫ 1͒ ͑2͒, or 2͑2x Ϫ 1͒ ͑x Ϫ 1͒.
QXP 46 Chapter R • 12/2/04 2:43 PM Page 46 Basic Concepts of Algebra 46. 11͙27 Ϫ 4͙3 29͙3 61. An equilateral triangle is shown below. 47. 6͙20 Ϫ 4͙45 ϩ ͙80 4͙5 48. 2͙32 ϩ 3͙8 Ϫ 4͙18 2͙2 49. 8͙2x 2 Ϫ 6͙20x Ϫ 5͙8x 2 3 Ϫ2x͙2 Ϫ 12͙5x 3 50. 2͙ 8x 2 ϩ 5͙ 27x 2 Ϫ 3͙x 3 a ͙3; 2 2 a (b) A ͙3 4 (a) h a 3 19͙ x 2 Ϫ 3x͙x 51. ͑ ͙3 Ϫ ͙2 ͒ ͑ ͙3 ϩ ͙2 ͒ 1 a 2 52. ͑ ͙8 ϩ 2͙5 ͒ ͑ ͙8 Ϫ 2͙5 ͒ Ϫ12 53. ͑ 2͙3 ϩ ͙5 ͒ ͑ ͙3 Ϫ 3͙5 ͒ Ϫ9 Ϫ 5͙15 54. ͑ ͙6 Ϫ 4͙7 ͒ ͑ 3͙6 ϩ 2͙7 ͒ Ϫ38 Ϫ 10͙42 55. ͑ 1 ϩ ͙3 ͒ 2 4 ϩ 2͙3 56. ͑ ͙2 Ϫ 5 ͒ 2 27 Ϫ 10͙2 57.