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6x 36 x 7. 36x 6x 6 x2 4. If 2 = .16 , then x equals x (A) (B) (C) (D) (E) 50 5 .5 .05 .005 8. x 2 + y 2 is equal to (A) (B) (C) (D) (E) x+y xy (x + y) (x  y)
x 2 + y2 none of these 143 144 Chapter 10 9. Divide 8 12 by 2 3 . (A) (B) (C) (D) (E) 16 9 8 12 96 10. ( 2 )5 is equal to (A) (B) (C) (D) (E) 2
22 4
42 8 www.petersons.com Roots and Radicals 145 1. ADDITION AND SUBTRACTION OF RADICALS
The conditions under which radicals can be added or subtracted are much the same as the conditions for letters in an algebraic expression. The radicals act as a label, or unit, and must therefore be exactly the same. In adding or subtracting, we add or subtract the coefficients, or rational parts, and carry the radical along as a label, which does not change. Example:
2 + 3 cannot be added 2 + 3 2 cannot be added 4 2 +5 2 = 9 2 Often, when radicals to be added or subtracted are not the same, simplification of one or more radicals will make them the same. To simplify a radical, we remove any perfect square factors from underneath the radical sign. Example:
12 = 4 ⋅ 3 = 2 3 27 = 9 ⋅ 3 = 3 3 If we wish to add 12 + 27 , we must first simplify each one. Adding the simplified radicals gives a sum of 5 3 . Example:
125 + 20 − 500 Solution:
25 ⋅ 5 + 4 ⋅ 5 − 100 ⋅ 5 = 5 5 + 2 5 − 10 5 = −3 5 www.petersons.com 146 Chapter 10 Exercise 1
Work out each problem. Circle the letter that appears before your answer. 1. Combine 4 27 − 2 48 + 147 (A) (B) (C) (D) (E) 2.
27 3 −3 3 93 10 3 11 3 80 + 45 − 20 4. Combine (A) (B) (C) (D) (E) 1 1 2 ⋅ 180 + ⋅ 45 − ⋅ 20 2 3 5 3 10 + 15 + 2 2
16 5 5 Combine (A) (B) (C) (D) (E)
95 55 −5 35 −2 5 97 24 5 5 none of these 5. Combine 5 mn − 3 mn − 2 mn (A) (B) (C) (D) (E) 0 1
mn 3. Combine 6 5 + 3 2 − 4 5 + 2 (A) (B) (C) (D) (E) 8
2 5+3 2 2 5+4 2 57 mn
− mn 5 www.petersons.com Roots and Radicals 147 2. MULTIPLICATION AND DIVISION OF RADICALS
In multiplication and division, we again treat the radicals as we would treat letters in an algebraic expression. They are factors and must be treated as such. Example:
2⋅ 3= 6 Example:
4 2 ⋅ 5 3 = 20 ⋅ 6...
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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 EmbryRiddle FL/AZ.
 Spring '10
 Colon
 SAT

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