Maya Bracy 8-1 1/14/11 ALGEBRA 2 MID TERM STUDY GUIDE B 1.3.1 -Estimating square roots to the nearest tenth: When estimating the value of a square root that isn't a perfect square... 1. You find the two perfect squares that the radical lies between 9< 15< 16 2. Find the two integers that the radical lies between 9 = 3 and 16 = 4 so… 3 < 15 < 4 3. Use a number line to visualize which integer is closest to the value of the radical
3 4 Because 15 is closer to 16 than 9, 15 is closer to 4 than it is to 3 4. Guess the value of the radical by increasing or decreasing the value of the integer. guess: 3.9 check: 3.9^2 = 15.21 too high guess: 3.8 check: 3.8^2 = 14.44 too low 5. Choose the answer with the closest value to the radical Because 15 is closer to 15.21 than to 14.44, 15 is closer to 3.9 than it is to 3.8 Answer: 15 3.9
NEXT SKILL B 1.3.2 -Simplifying radical expressions To simplify expressions with radicals you must know: Product Property of Square Roots: ab = a * b Quotient Property of Square Roots: a/b = a / b Use these properties to help to simplify radical expressions
Example 1: -200 Using the product property of square roots find a perfect square that is also a factor of 200 -100*2 = 100 * 2 Simplify this expression 100 = 10 Answer: -102
Example 2: 36/121 Using the quotient property of square roots write the expression in a simpler form 36 / 121 Simplifying this expression 36 = 6 and 121 = 11 Answer: 6/11
Example 3: 12 * 3 First factor 12 4*3 * 3 Using the product property of square roots write the expression in a simpler form 4 * 3 * 3 Simplify this expression 4 = 2 2 * 3 * 3
3 * 3 = 9 2 * 9 9 = 3 2 * 3 Answer: 6 For extra help go to: http://my.hrw.com/math06_07/nsmedia/homework_help/alg2/alg2_ch01_03_homeworkhelp.html