2-9 Square Roots and Cube Roots notes

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