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Name:____________________ . 1 = 2 = Pre-Algebra 5.0 ~ Note Sheets Chapter 9 Lessons 1 and 2 Square Roots and Real Numbers 3 = Lesson One: To find square roots and to estimate square roots 4 = Perfect squares: 5 = whole numbers (examples: 25, 49, 81, 100) 6 = 7 = Square root: a number that is one of two equal factors of the number 8 = 9 = numbers that are squares of Radical sign: , used to indicate the square root 10 = Examples: Find each square root. 11 = 1. 25 2. 64 3. 4. 0.04 5. 1.96 6. 36 12 = 13 = 14 = 15 = 1 Estimate the square root AND give the two integers each square root falls between. Show your estimation work! 1. _____ < 8 < _____ 2. _____ < 67 < _____ 3. _____ < 95.3 < _____ estimate: _________ integers: _______________ 4. _____ < 12 < _____ estimate: __________ integers: _______________ 5. _____ < 123 < _____ estimate: _________ integers: _______________ estimate: ___________ integers: _______________ estimate: __________ integers: _______________ Lesson Two: To identify and compare numbers in the real number system and to solve equations by finding square roots Natural numbers (Counting numbers): Whole numbers: Integers: 1, 2, 3, . . . 0, 1, 2, 3, . . . . . . , -3, -2, -1, 0, 1, 2, 3, . . . Rational numbers: all numbers that can be written in the a form b including terminating decimals and repeating decimals Irrational numbers: numbers that cannot be written as a fraction; numbers that are not repeating or terminating decimals (they go on forever with no pattern) Real Numbers: the set of rational and irrational numbers Examples: Determine whether each statement is sometimes, always, or never true. 1. A rational number is a whole number. 2. Zero is a natural number. REAL RATIONAL INTEGERS INTEGERS …, -3, -2, -1, 0, 1, 2, 3,… IRRATIONAL WHOLE 0, 1, 2, 3, … 0.1749... NATURAL 1,2,3,… 2 1 0 .5 2 1 0. 3 3 For each number, put an X in the box if it belongs to that set of numbers. Natural 3. 12 4. -5 1 9 5. 6. 7. 31 24 8 8. 6.54 9. 0.050050005… Whole Integer Rational Irrational Real Choose the symbol to replace ● to make a true sentence. 10. 9 2 .1 a. 11. < b. = c. > b. = c. > 94.6 10 a. < Order the integers in each set from least to greatest. 12. 1 36 49 , 7 , , 7.27 4 5 Solve each equation. Round to the nearest tenth, if necessary. Give your answer as an equation. 13. a 2 64 14. e 2 81 15. f 2 0.49 Work for 9.1 Worksheet: 34. _____ < 38 < _____ 36. _____ < 389 < _____ estimate: _________ integers: _______________ 38. _____ < 118 < _____ estimate: _________ integers: _______________ 40. _____ < 83 < _____ 42. _____ < 119 < _____ 44. _____ < estimate: _________ integers: _______________ estimate: _________ integers: _______________ estimate: _________ integers: _______________ 27.5 < _____ estimate: _________ integers: _______________ Work for 9.2 Worksheet: Natural 2. 4. 25 1 8 6. 0.343434… 8. 10. 7 32 4 12. 24.6 14. 0 Whole Integer Rational Irrational Real