Numerical Roots and Radicals Chapter Questions



Numbers & Operations 8th Grade Chapter QuestionsWhat are the properties of a square?What does taking the square root have to do with the area of a square?Why is it helpful to memorize perfect squares?What can be helpful when finding the square roots of numbers greater than 400?Explain how to take the square root of a fraction or a decimal.Explain how to approximate a square root.What is the difference between an irrational and rational number?Explain how to convert between the different forms of a rational number.Numbers & Operations Chapter ProblemsConverting Repeating Decimals to Fractions and Decimal ExpansionClassworkWrite each repeating decimal as a fraction in simplest form*0.70.245.613.51.1236.9Find the decimal expansion of the following*:4155121320138325145HomeworkWrite each repeating decimal as a fraction in simplest form*0.430.82.724.361.2343.9Find the decimal expansion of the following*:58173021552416089Squares, Square Roots & Perfect SquaresClassworkA square has an area of 9 units2.What is the side length of a square of this area?Draw a square with an area of 9 units2.What is the square root of 9?Explain why your answers in parts (a) and (c) are the same.Fill in the following table:Side Length of a square(units)Area of the square(units2)12345678910111213Explain how the table above helps you find the square root of 121?Simplify each square root.25 64 81 49 16 HomeworkA square has an area of 36 units2.What is the side length of a square of this area?Draw a square with an area of 36 units2.What is the square root of 36?Explain why your answers in parts (a) and (c) are the same.Fill in the following table:Side Length of a square(units)Area of the square(units2)14151617181920Simplify each square root.289400196361144Squares of Numbers Greater Than 20ClassworkFill in the following table:Side Length of a square(units)Area of the square(units2)102030405060708090100If you compare that to the table of side lengths from 1-10, what pattern do you notice?Simplify each square root.2809 7921 484 6400 2025 225 841 9409 961 4356 HomeworkSimplify each square root.5041 1296 8464 3025 3721 6889 576 2401 2500 289 Simplifying Perfect Square Radical ExpressionsClassworkSimplify each square root.25 64 -81 -81 49 2549-16121361442549-25100.64.0081-.25.0016-.04HomeworkSimplify each square root.289 QUOTE -400 QUOTE 64 QUOTE 361 QUOTE -10000 QUOTE 25225 QUOTE 49196-81400-366410010000-.09-.0196.49 QUOTE .0361 QUOTE .25 QUOTE Approximating Square RootsClassworkWhat two integers do the following square roots fall between?68 149 5 52 105 Draw and label a number line from 0 to 10. Place the following square roots on the number line.56 97 11 316 Estimate the following square roots.6 70 55 14 106 41 80 65 8 233 Approximate the square root to the nearest integer For what integer x is x closest to 7.42?*For what integer x is x closest to 5.1?*For what integer x is x closest to 3.9?*HomeworkWhat two integers do the following square roots fall between?158 12 99 66 175 Draw and label a number line from 0 to 10. Place the following square roots on the number line.39 84 14 2158 Estimate the following square roots.78 7 63 29 42 138 300 148 21 52Approximate the square root to the nearest integera.b. c.d.e. For what integer x is x closest to 5.2?*For what integer x is x closest to 6.1?*For what integer x is x closest to 6.9?*Rational & Irrational NumbersClasswork. Circle the numbers below that are rational3.56 π1310 -49108 0.252150.4Given the statement “If x is a rational number then x is irrational.” Which values of x make the statement false?* A) 15 B) 24 C) 4 D) 20Given the statement “If x is a rational number then x is irrational.” Which values of x make the statement false?* A) 25 B) 49 C) 5 D) 59HomeworkCircle the numbers below that are irrational.38 QUOTE 7 QUOTE 81 QUOTE 6.7589 QUOTE 121 QUOTE 61 QUOTE π225 QUOTE 0.18 Given the statement “If x is a rational number then x is irrational.” Which values of x make the statement false?* A) 36 B) 8 C) 16 D) 121Given the statement “If x is a rational number then x is irrational.” Which values of x make the statement false?* A) 144 B) 12 C) 48 D)30 QUOTE Properties of ExponentsClassworkComplete each equation for the missing value:(52)(55) = 5?(127)(123) = 12?(3-2)(35) = 3?(49)(4-3) = 4?(54)(5?) = 512(107)(10?)(10-6) = 10334 ÷ 32 = 3?= 5? = 9?124 ÷ 126 = 12?108 ÷ 10? = 103= 24A rectangle has a length of 515mm and a width of 512mm. Write an expression for the area of the rectangle as a power of 5.*Express the volume of a cube with a side length of 74inches as a power of 7.*a) Write an exponential expression for the area of a rectangle with a length of 10-5meters and a width of 10-7meters. b) Evaluate the expression to find the area of the rectangle.*HomeworkComplete each equation for the missing value:(122)(127) = 12?(25)(22) = 2?(5-3)(55) = 5?(158)(15-5) = 15?(67)(6?) = 615(11-6)(11?)(118) = 11577 ÷ 73 = 7?= 11?37 ÷ 39 = 3? = 2?= 1325? ÷ 56 = 53 A rectangle has a length of 48mm and a width of 46mm. Write an expression for the area of the rectangle as a power of 4.*Express the volume of a cube with a side length of 25inches as a power of 2.*a) Write an exponential expression for the area of a rectangle with a length of 7-2 meters and a width of 7-4meters. b) Evaluate the expression to find the area of the rectangle.*Roots & Radicals ReviewDetermine whether the given numbers are perfect squares. Circle your answer.1 Yes No8 Yes No16 Yes No25 Yes No82 Yes NoCircle the simplified version of each square root: 144 1412722136100a. 10b. 6c. 0.6d. 18-.0049 a. -7b. 0.7c. 0.07d. -0.07Circle whether the given number is rational or irrational π rational irrational 0.875 rational irrational )39 rational irrationalBetween what two integers does the following square root fall? 454 & 56 & 77 & 85 & 6(47)(43) = 4?102445Approximate 47 ________Find the missing value 114 ÷ 116 = 11? ____________________ 3733=3?________________ (67)(6-2) = 6?A rectangle has a length of 410cm and a width of 48cm. What is the area of the rectangle written as a power of 4? ___________________Draw and label a number line from 0-10. Place the following numbers on the number line:* 28, 30, 82Write 0.65 as a fraction in simplest form.*Write 1.423 as a fraction in simplest form.* Write two exponential expressions with like bases. Leave all answers in simplified exponential form.Expression 1:Expression 2:Multiply your expressions.Divide your expressionsRaise your first expression to the 5th power. ................
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