Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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482 Chapter 5 Quadratic Functions Version: Fall 2007 x = ± 5 These solutions are called square roots of 25. Because there are two solutions, we need a different notation for each. We will denote the positive square root of 25 with the notation 25 and the negative square root of 25 with the notation 25 . Thus, 25 = 5 and 25 = 5 . In a similar vein, the equation x 2 = 36 has two solutions, x = ± 36 , or alternatively, x = ± 6 . The notation 36 calls for the positive square root, while the notation 36 calls for the negative square root. That is, 36 = 6 and 36 = 6 . It is not necessary that the right-hand side of the equation x 2 = a be a “perfect square.” For example, the equation x 2 = 7 has solutions x = ± 7 . (4) There is no rational square root of 7. That is, there is no way to express the square root of 7 in the form p/q , where p and q are integers. Therefore, 7 is an example of an irrational number. However, 7 is a perfectly valid real number and we’re perfectly comfortable leaving our answer in the form shown in equation (4) .
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