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8-2 Estimating Roots Objective: Students will be able to use roots to estimate solutions. 8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. Do Now: Write The Following In Exponential Form Then Solve: 1) 4*4 2) 3*3*3 3) 5*5*5 4) 6*6 5) 7*7 6) -10*-10*-10 7) -2.5*-2.5 2 x Squaring: to raise a number to the second power Cubing: to raise a number to the third power. x x 2 Square Root: one of the two equal factors of a number 3 3 x 3 Cube Root: one of the three equal factors of a number Perfect Square: a rational number whose square root is a whole number x a 2 ax (5) 25 2 25 5 Non-Perfect Square: a number whose square root is not a whole number (decimal/fraction) 13 3.6055... Perfect Cube: a rational number whose cube root is a whole number x a 3 3 2 8 ax 3 3 8 2 Non-Perfect Cube: a number whose cube root is not a whole number (decimal, fraction) 3 14 2.4101... Find Each Square or Cube Root Perfect Square Roots Perfect Cube Roots Estimating Square and Cube Roots: You can estimate the value of a square or cube root by determining which two perfect squares or cubes the number falls in between. Estimate 3 100 83 Worksheets! Homework 8-2 Pages 85-86 All #’s Exit Ticket: After an accident, officials used the formula below to estimate the speed the car was traveling based on the length of the car’s skid marks. Where s represents the speed in miles per hour and m is the length of the skid marks in feet. s 24m If a car leaves a skid mark of 50 feet, what was its approximate speed?