Section 1.7 Exponents, Algebraic Expressions, and the Order of Operations 59 One important application of exponents lies in recognizing powers of 10, that is, 10 raised to a whole-number power. For example, consider the following expressions. 101 10 102 10 10 100 103 10 10 10 1000 104 10 10 10 10 10,000 105 10 10 10 10 10 100,000 From these examples, we see that a power of 10 results in a 1 followed by several zeros. The number of zeros is the same as the exponent on the base of 10. 2. Square Roots To square a number means that we multiply the base times itself. For example, To find a positive square root of a number means that we reverse the process of squaring. For example, finding the square root of 25 is equivalent to asking, “What positive number, when squared, equals 25?” The symbol (called a radical sign), is used to denote the positive square root of a number. Therefore, is the positive number, that when squared, equals 25. Thus, because Evaluating Square Roots Example 2 Find the square roots. a. b. c. d. Solution: a. because b. because c. because d. 10 0 because 1022 0 0 0 19 164 11 10 19 3 1322 3 3 9 164 8 1822 8 8 64 11 1 1122 1 1 1 125 5 1522 25. TIP: To simplify square roots, it is advisable to become familiar with these squares and square roots. 02 0 10 0 72 49 149 7 12 1 11 1 82 64 164 8 22 4 14 2 92 81 181 9 32 9 19 3 102 100 1100 10 42 16 116 4 112 121 1121 11 52 25 125 5 122 144 1144 12 62 36 136 6 132 169 1169 13 125 1 52 5 5 25. 106 10 10 10 10 10 10 1,000,000 Skill Practice Find the square roots. 4. 14 5. 1100 6. 1400 7. 1121 Answers 4. 2 5. 10 6. 20 7. 11
miller_prealgebra_2e_ch1_3
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