Problem 1SP: Identify the square roots of the real numbers.
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Problem 2SP: Identify the square roots of the real numbers. 16 Problem 3SP: Identify the square roots of the real numbers. 1 Problem 4SP: Identify the square roots of the real numbers.
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Problem 5SP: Simplify the square roots. 81 Problem 6SP: Simplify the square roots.
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Problem 7SP: Simplify the square roots. 0.09 Problem 8SP: Simplify the square roots, if possible. − 81 Problem 9SP: Simplify the square roots, if possible. − 64 Problem 10SP: Simplify the square roots, if possible. − 0.25 Problem 11SP: Simplify the square roots, if possible.
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Problem 12SP: Simplify if possible. 16 4 Problem 13SP: Simplify if possible.
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Problem 14SP: Simplify if possible. − 1 5 Problem 15SP: Simplify if possible.
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Problem 16SP: Simplify if possible.
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Problem 17SP: Simplify if possible. − 36 Problem 18SP: Simplify if possible. − 27 3 Problem 19SP: Simplify the expressions.
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Problem 20SP: Simplify the expressions. ( − 4 ) 3 3 Problem 21SP: Simplify the expressions. ( y + 9 ) 2 Problem 22SP: Simplify the expressions. ( t + 1 ) 3 3 Problem 23SP: Simplify the expressions. v 8 4 Problem 24SP: Simplify the expressions. Assume all variables represent positive real numbers. t 6 Problem 25SP: Simplify the expressions. Assume all variables represent positive real numbers. 64 y 12 3 Problem 26SP: Simplify the expressions. Assume all variables represent positive real numbers. x 4 y 4 4 Problem 27SP: Simplify the expressions. Assume all variables represent positive real numbers. − 32 a 5 b 10 5 Problem 28SP: Use the Pythagorean theorem and the definition of the principal square root to find the length of... Problem 29SP: Two cars leave the same place at the same time. One travels west at 40 mph, and the other travels... Problem 30SP: For each function, write the domain in interval notation. f ( x ) = x + 5 Problem 31SP: For each function, write the domain in interval notation. g ( t ) = t − 9 3 Problem 32SP: For each function, write the domain in interval notation. h ( a ) = 1 − 2 a Problem 33SP: 33. Given
a. Write the domain ofin interval notation.
b. Graph by making a table of ordered... Problem 1PE Problem 2PE: Simplify the expression 8 3 . Explain how you can check your answer. Problem 3PE: a. Find the square roots of 64. (See Example 1.) b. Find 64 . c. Explain the difference between the... Problem 4PE: a. Find the square roots of 121. b. Find 121 . c. Explain the difference between the answers in part... Problem 5PE: a. What is the principal square root of 81? b. What is the negative square root of 81? Problem 6PE: a. What is the principal square root of 100? b. What is the negative square root of 100? Problem 7PE: Using the definition of a square root, explain why − 36 is not a real number. Problem 8PE: For Exercises 8–19, evaluate the roots without using a calculator. Identify those that are not real... Problem 9PE: For Exercises 8–19, evaluate the roots without using a calculator. Identify those that are not real... Problem 10PE: For Exercises 8–19, evaluate the roots without using a calculator. Identify those that are not real... Problem 11PE: For Exercises 8–19, evaluate the roots without using a calculator. Identify those that are not real... Problem 12PE: For Exercises 8–19, evaluate the roots without using a calculator. Identify those that are not real... Problem 13PE: For Exercises 8–19, evaluate the roots without using a calculator. Identify those that are not real... Problem 14PE: For Exercises 8–19, evaluate the roots without using a calculator. Identify those that are not real... Problem 15PE: For Exercises 8–19, evaluate the roots without using a calculator. Identify those that are not real... Problem 16PE: For Exercises 8–19, evaluate the roots without using a calculator. Identify those that are not real... Problem 17PE: For Exercises 8–19, evaluate the roots without using a calculator. Identify those that are not real... Problem 18PE: For Exercises 8–19, evaluate the roots without using a calculator. Identify those that are not real... Problem 19PE: For Exercises 8–19, evaluate the roots without using a calculator. Identify those that are not real... Problem 20PE: Using the definition of an n th root, explain why − 16 4 is not a real number. Problem 21PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 22PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 23PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 24PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 25PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 26PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 27PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 28PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 29PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 30PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 31PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 32PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 33PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 34PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 35PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 36PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 37PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 38PE: For Exercises 21–38, evaluate the roots without using a calculator. Identify those that are not real... Problem 39PE: For Exercises 39–58, simplify the radical expressions. (See Example 5.)
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Problem 40PE: For Exercises 39–58, simplify the radical expressions.(See Example 5.) a 4 4 Problem 41PE: For Exercises 39–58, simplify the radical expressions. (See Example 5.)
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Problem 42PE: For Exercises 39–58, simplify the radical expressions.(See Example 5.) a 5 5 Problem 43PE: For Exercises 39–58, simplify the radical expressions. (See Example 5.)
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Problem 44PE: For Exercises 39–58, simplify the radical expressions. (See Example 5.)
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Problem 45PE: For Exercises 39–58, simplify the radical expressions. (See Example 5.)
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Problem 46PE: For Exercises 39–58, simplify the radical expressions.(See Example 5.) ( y + 3 ) 3 3 Problem 47PE: For Exercises 39–58, simplify the radical expressions.(See Example 5.) x 2 y 4 Problem 48PE: For Exercises 39–58, simplify the radical expressions. (See Example 5.)
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Problem 49PE: For Exercises 39–58, simplify the radical expressions.(See Example 5.) − x 3 y 3 3 , y ≠ 0 Problem 50PE: For Exercises 39–58, simplify the radical expressions.(See Example 5.) a 4 b 8 4 , b ≠ 0 Problem 51PE: For Exercises 39–58, simplify the radical expressions. (See Example 5.)
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Problem 52PE: For Exercises 39–58, simplify the radical expressions. (See Example 5.)
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Problem 53PE: For Exercises 39–58, simplify the radical expressions.(See Example 5.) ( − 92 ) 3 3 Problem 54PE: For Exercises 39–58, simplify the radical expressions. (See Example 5.)
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Problem 55PE: For Exercises 39–58, simplify the radical expressions. (See Example 5.)
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Problem 56PE: For Exercises 39–58, simplify the radical expressions.(See Example 5.) ( − 2 ) 5 5 Problem 57PE: For Exercises 39–58, simplify the radical expressions.(See Example 5.) ( − 923 ) 7 7 Problem 58PE: For Exercises 39–58, simplify the radical expressions.(See Example 5.) ( − 417 ) 6 6 Problem 59PE: For Exercises 59–74, simplify the expressions. Assume all variables are positive real numbers. (See... Problem 60PE: For Exercises 59–74, simplify the expressions. Assume all variables are positive real numbers. (See... Problem 61PE: For Exercises 59–74, simplify the expressions. Assume all variables are positive real numbers. (See... Problem 62PE: For Exercises 59–74, simplify the expressions. Assume all variables are positive real numbers. (See... Problem 63PE: For Exercises 59–74, simplify the expressions. Assume all variables are positive real numbers. (See... Problem 64PE: For Exercises 59–74, simplify the expressions. Assume all variables are positive real numbers. (See... Problem 65PE: For Exercises 59–74, simplify the expressions. Assume all variables are positive real numbers. (See... Problem 66PE: For Exercises 59–74, simplify the expressions. Assume all variables are positive real numbers. (See... Problem 67PE: For Exercises 59–74, simplify the expressions. Assume all variables are positive real numbers. (See... Problem 68PE: For Exercises 59–74, simplify the expressions. Assume all variables are positive real numbers. (See... Problem 69PE: For Exercises 59–74, simplify the expressions. Assume all variables are positive real numbers. (See... Problem 70PE: For Exercises 59–74, simplify the expressions. Assume all variables are positive real numbers. (See... Problem 71PE Problem 72PE: For Exercises 59–74, simplify the expressions. Assume all variables are positive real numbers. (See... Problem 73PE: For Exercises 59–74, simplify the expressions. Assume all variables are positive real numbers. (See... Problem 74PE: For Exercises 59–74, simplify the expressions. Assume all variables are positive real numbers. (See... Problem 75PE: For Exercises 75–78, find the length of the third side of each triangle by using the Pythagorean... Problem 76PE: For Exercises 75–78, find the length of the third side of each triangle by using the Pythagorean... Problem 77PE: For Exercises 75–78, find the length of the third side of each triangle by using the Pythagorean... Problem 78PE: For Exercises 75–78, find the length of the third side of each triangle by using the Pythagorean... Problem 79PE: For Exercises 79–82, use the Pythagorean theorem. Roberto and Sherona began running from the same... Problem 80PE: For Exercises 79–82, use the Pythagorean theorem. Leine and Laura began hiking from their... Problem 81PE: For Exercises 79–82, use the Pythagorean theorem. Two mountain bikers take off from the same place... Problem 82PE: For Exercises 79–82, use the Pythagorean theorem. Professor Ortiz leaves campus on her bike, heading... Problem 83PE: For Exercises 83–86, evaluate the function for the given values of x. Then write the domain of the... Problem 84PE: For Exercises 83–86, evaluate the function for the given values of x. Then write the domain of the... Problem 85PE: For Exercises 83–86, evaluate the function for the given values of x. Then write the domain of the... Problem 86PE: For Exercises 83–86, evaluate the function for the given values of x. Then write the domain of the... Problem 87PE: For each function defined in Exercises 87–94, write the domain in interval notation. (See Example... Problem 88PE: For each function defined in Exercises 87–94, write the domain in interval notation. (See Example... Problem 89PE: For each function defined in Exercises 87–94, write the domain in interval notation. (See Example... Problem 90PE: For each function defined in Exercises 87–94, write the domain in interval notation. (See Example... Problem 91PE: For each function defined in Exercises 87–94, write the domain in interval notation. (See Example... Problem 92PE: For each function defined in Exercises 87–94, write the domain in interval notation. (See Example... Problem 93PE: For each function defined in Exercises 87–94, write the domain in interval notation. (See Example... Problem 94PE: For each function defined in Exercises 87–94, write the domain in interval notation. (See Example... Problem 95PE: For Exercises 95–102,
a. Write the domain of in interval notation.
b. Graph by making a table of... Problem 96PE: For Exercises 95–102, a. Write the domain of f in interval notation. b. Graph f by making a table of... Problem 97PE: For Exercises 95–102, a. Write the domain of f in interval notation. b. Graph f by making a table of... Problem 98PE: For Exercises 95–102,
a. Write the domain of in interval notation.
b. Graph by making a table of... Problem 99PE: For Exercises 95–102, a. Write the domain of f in interval notation. b. Graph f by making a table of... Problem 100PE: For Exercises 95–102,
a. Write the domain of in interval notation.
b. Graph by making a table of... Problem 101PE: For Exercises 95–102,
a. Write the domain of in interval notation.
b. Graph by making a table of... Problem 102PE: For Exercises 95–102, a. Write the domain of f in interval notation. b. Graph f by making a table of... Problem 103PE: For Exercises 103–106, write the English phrase as an algebraic expression.
103. The sum of q and... Problem 104PE: For Exercises 103–106, write the English phrase as an algebraic expression. The product of 11 and... Problem 105PE: For Exercises 103–106, write the English phrase as an algebraic expression.
105. The quotient of 6... Problem 106PE: For Exercises 103–106, write the English phrase as an algebraic expression. The difference of y and... Problem 107PE: 107. If a square has an area of 64, then what are the lengths of the sides?
Problem 108PE:
108. If a square has an area of, then what are the lengths of the sides?
Problem 109PE: For Exercises 109–116, use a calculator to evaluate the expressions to four decimal places. 69 Problem 110PE: For Exercises 109–116, use a calculator to evaluate the expressions to four decimal places. 5798 Problem 111PE: For Exercises 109–116, use a calculator to evaluate the expressions to four decimal places.
111.
Problem 112PE: For Exercises 109–116, use a calculator to evaluate the expressions to four decimal places.
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Problem 113PE: For Exercises 109–116, use a calculator to evaluate the expressions to four decimal places. 7 25 4 Problem 114PE: For Exercises 109–116, use a calculator to evaluate the expressions to four decimal places. − 3 9 3 Problem 115PE: For Exercises 109–116, use a calculator to evaluate the expressions to four decimal places. 3 − 19... Problem 116PE: For Exercises 109–116, use a calculator to evaluate the expressions to four decimal places.
116.
Problem 117PE: 117. Graph. Use the graph to confirm the domain found in Exercise 83.
Problem 118PE: 118. Graph. Use the graph to confirm the domain found in Exercise 84.
Problem 119PE: Graph g ( x ) = x − 2 3 . Use the graph to confirm the domain found in Exercise 85. Problem 120PE: Graph f ( x ) = x + 1 3 . Use the graph to confirm the domain found in Exercise 86. format_list_bulleted
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