New SAT Math Workbook

2 62 wwwpetersonscom 148 chapter 10 3 simplifying

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Unformatted text preview: Example: (3 2 )2 = 3 2 ⋅ 3 2 = 9 ⋅ 2 = 18 Example: 8 2 = 4=2 Example: 10 20 24 =5 5 Example: 2 ( 8 + 18 ) = 16 + 36 = 4 + 6 = 10 Exercise 2 Work out each problem. Circle the letter that appears before your answer. 1. Multiply and simplify: 2 18 ⋅ 6 2 (A) 72 (B) 48 (C) 12 6 (D) 8 6 (E) 36 Find 3 3 (A) (B) (C) (D) (E) 3. 4. Divide and simplify: (A) (B) (C) (D) (E) 5. 2b 2b 32b 3 8b 2b 2b 2 2. () 81 93 3 b 2b Divide and simplify: (A) (B) (C) (D) (E) 73 7 12 11 3 12 3 40 3 15 96 52 27 3 81 3 243 1 1 2( 6 + 2) 2 2 Multiply and simplify: (A) (B) (C) (D) (E) 3+ 1 2 1 ⋅3 2 6 +1 1 6+ .2 6+2 www.petersons.com 148 Chapter 10 3. SIMPLIFYING RADICALS CONTAINING A SUM OR DIFFERENCE In simplifying radicals that contain several terms under the radical sign, we must combine terms before taking the square root. Example: 16 + 9 = 25 = 5 It is not true that 16 + 9 = 16 + 9 , which would be 4 + 3, or 7. Example: x2 x2 − = 16 25 25 x 2 − 16 x 2 9 x 2 3x = = 400 400 20 Exercise 3 Work out each problem. Circle the letter that appears before your answer. 1. Simplify (A) (B) (C) (D) (E) 2. 25 x 2 144 5x 12 5x 2 12 x 7 7x 12 36 y 2 + 64 x 2 x2 x2 + 9 16 4. Simplify (A) (B) (C) (D) (E) 2y 3 y 5 10 y 3 y3 6 y2 y2 − 2 18 cannot be done 5. a 2 + b 2 is equal to Simplify (A) (B) (C) (D) (E) 6y + 8x 10xy 6y2 + 8x2 10x2y2 cannot be done x2 x2 − 64 100 (A) (B) (C) (D) (E) a+b a–b a2 + b2 (a + b) (a - b) none of these 3. Simplify (A) (B) (C) (D) (E) x 40 x − 2 x 2 3x 40 3x 80 www.petersons.com Roots and Radicals 149 4. FINDING THE SQUARE ROOT OF A NUMBER In finding the square root of a number, the first step is to pair off the digits in the square root sign in each direction from the decimal point. If there is an odd number of digits before the decimal point, insert a zero at the beginning of the number in order to pair digits. If there is an odd number of digits after the decimal point, add a zero at the end. It should be clearly understood that these zeros are place holders only and in no way change the value of the number. Every pair of numbers in the radical sign gives one...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at Embry-Riddle FL/AZ.

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