Estimating Square Roots to the Nearest Tenth

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: -102

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