2-9 Square Roots and Cube Roots notes

Warm-Up1. Solve 4a – 1.6 = 3.8 2. Solve 20 = -5.4b + 3.8a = 1.35 b = -3Find the area of each square.3. 4.13 2 =169cm 2 7 2 =49cm 213 cm7 mChange each decimal to a fraction or mixed number. Write thefraction part of each answer in lowest term.5. 0.875 = 7 87. 2.25 = 2 1 46. 0.66 = 2 38. 7.08 = 7 2 25Integrated 1 2-9 Square Roots and Cube Roots 12-9 Square Roots & Cube RootsTypes of Numbers• Rational numbers - a number that can be writtenas a quotient of two integers1Since − = − = − 105 . , − 05 . is a rational number2 2• Irrational numbers - a number that cannot bewritten as a quotient of two integersSince 2 cannot be written as a quotient of twointegers, 2 is an irrational number.• Real numbers - any rational or irrational numberπ is an irrational number, so π is a real number.Integrated 1 2-9 Square Roots and Cube Roots 22-9 Square Roots & Cube RootsTell whether each number is rational or irrational.25 25 = 5, rational, integer86 .144 .− 886 . = 8 2 , rational, repeating decimal3144 . = 12 . , rational, terminating decimal− 8 = − 4⋅ 2 = −2 2, irrationalNon-terminating &non-repeating decimal2-9 Square Roots & Cube RootsSquare Roots• One of two equal factors of a number• Every positive number has both a positive and anegative square root.• Both 5 and –5 are square roots of 25• is the symbol for square root.• Perfect square – a number whose square roots are integers• 64 =± 8 , so 64 is a perfect square.Integrated 1 2-9 Square Roots and Cube Roots 3Integrated 1 2-9 Square Roots and Cube Roots 42-9 Square Roots & Cube RootsFind the square roots of each number001 . ± 001 . = ± . 1625 . ± 625 . = ± 25 .121 ± 121 = ± 111491 1± = ±49 72-9 Square Roots & Cube RootsEstimate each square root within a range of twointegers. Then use a calculator to find eachsquare root to the nearest hundredth.12 12 is between 3 and 472 72 is between 8 and 990 90 is between 9 and 10Integrated 1 2-9 Square Roots and Cube Roots 5Integrated 1 2-9 Square Roots and Cube Roots 61

2-9 Square Roots & Cube RootsCube Roots• One of three equal factors of a number• Since 3·3·3=27, 3 is a cube root of 27.• 3stands for cube root.• Perfect cube – a number whose cube root is aninteger3• 125 = 5 , so 125 is a perfect cube.2-9 Square Roots & Cube RootsEstimate35 between two integers. Then use a calculator.3 35is between 1 and 2. 5 ≈ 171 .Integrated 1 2-9 Square Roots and Cube Roots 7Integrated 1 2-9 Square Roots and Cube Roots 82-9 Square Roots & Cube RootsSolving square root equationsThe area of a square is 29 cm 2 . Find the length of a side ofthe square.• If you know the area of a square then use the formulaA = s 2 to find the length of each side.29 = s 229 = s 2 = 5.39s = 5.39 cmLength must be positive, so only the positive square root make sense.Integrated 1 2-9 Square Roots and Cube Roots 92-9 Square Roots & Cube RootsSolving cube root equationsThe volume of a cube is 650 in 3 . Find the length of anedge of the cube.• If you know the volume of a cube, then use the formulaV = s 3 to find the length of each edge.650 = s 33650 = s = 8.663 3s = 8.66 in.Integrated 1 2-9 Square Roots and Cube Roots 10Simplify1. 6rt + 8r −rt −5t2. ( 3x)( 5x)( x)3. 3z − 5z + 8z + 9z4 2 2Quiz5rt + 8r - 5t15x 33z 4 + 4z 2 + 8zWrite and solve an equation to find the unknown angle measureSolve4. 5. x° x°x°6. m5 − 1= −2m = -550°29°x = -450 + 2x = 180 7. 5x + 7x = -48x + 29 = 908. 24 = 5x + 3x x = 3x = 61° x = 65° 9. 7 = 15 + 16a a = -1/2Integrated 1 2-9 Square Roots and Cube Roots 112