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Chapter 1 Test: October 24 Review 3 Previous Study Guides (on website) Roots (Lesson 8) Examples: √64 = 8 (Since 8 x 8 = 64) −√4 = -2 Don't let the sign out front confuse you! Just find the square root of the number and bring the sign in front down! What is the square root of 4? 2 Rewrite the answer with the sign. -2 ±√1.21 = ± 1.1 When there's a decimal in the number, look at the number without a decimal point there. 121. Is there a square root of 121? Yes! = 11 Because there's a decimal in the original number, you're going to have to put a decimal in the solution. 1.1 Leave the sign on the outside in your solution too. We read that as "plus or minus." T2 = 169 We need to solve this equation. Remember, when solving any equation, whatever we do to one side, we do to the other. To cancel out something being “squared” we take the “square root” √169 = ±13 T= ±13 Estimating with Roots (Lesson 9) Examples: Estimate √83 We know 83 is not a “perfect square.” This means that no whole number can be multiplied by itself to get 83. The closest perfect square less than 83 is 81. The closest perfect square greater than 83 is 100. √81 = 9 √100 = 10……… so the √83 is between 9 and 10. Since 83 is closer to 81 than 100 the SQUARE ROOT of 83 is closer to 9. Therefore the BEST ESTIMATE would be 9. Estimate √320 3 We know 320 is not a “perfect cube.” This means that no whole number can be multiplied by itself three times to get 320. The closest perfect cube less than 320 is 216. The closest perfect cube greater than 320 is 343. √216= 6 (6x6x6=216) 3 √343 = 7 (7x7x7=343) ……… so the √320 is 3 3 between 6 and 7. Since 320 is closer to 343 than 216 the CUBE ROOT of 320 is closer to 7. Therefore the BEST ESTIMATE would be 7. Comparing Real Numbers (Lesson 10) We know what a rational number is (any number that can be written as a fraction). They include Whole Numbers, Integers, and Natural Numbers. An irrational number is a number that is NOT rational- it cannot be written as a fraction REAL NUMBERS are the sets of rational and irrational numbers combined. Examples: Name all the sets of numbers (types of numbers) each REAL NUMBER belongs to: 0.25252525… = Rational Number because it is a repeating decimal but can be rewritten as the fraction 25 99 . √36… = Natural Number, Whole Number, Integer, AND Rational Number because √36 = 6. -√7… = -2.645751311…..Irrational Number because it does not end or repeat. Comparing and Ordering Real Numbers **BEFORE you can compare or order you must make them the SAME TYPE of numbers. Write numbers in decimal form in order to compare or order. Examples: √7 ______2 2 3 √7 = 2.645751311… 2 2 = 2.66666666666… 3 2 Since 2.645 is less than 2.6666 √7 < 2 3 15.7% ______√0.02 15.7% = 0.157 √0.02= 0.141 Since 0.157 is greater than 0.141 15.7% > √0.02 4 Order the set {√30, 6, 5 , 5.3} from least to greatest. 5 √30 = 5.48 6= 6.00 4 5 = 5.80 5 5.3 = 5.3 Since 5.3 < 5.48 < 5.80 < 6.00 The order from least to greatest is 4 5.3, √30, 5 5 , 6