Math 154 :: Elementary Algebra

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Clifton Tate
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1 Math :: Elementary Algebra Section 9. Section 9. Section 9. Section 9. Section 9. Section 9.6

2 Math :: Elementary Algebra Section 9. Introduction to Square Roots. This answer should be in your own words.. This answer should be in your own words.. No, the square root of a negative number does NOT have a real number value.. The epression under the square root sign is called the radicand not a real number not a real number a) b) 6 c) d) e) 9 f) (The negative sign in front of the makes the negative -value positive.) g) h) i) Section 9. Answers

3 Math :: Elementary Algebra Section 9. Simplifying Radical Epressions Part I. This answer should be in your own words.. When factors are pulled out from a square root, multiplication is between those factors and the factors that remain under the square root.. If the radicand in a square root epression has a variable raised to an eponent, the short cut rule for simplifying the square root for that variable is to divide the eponent by.. This answer should be in your own words.. a) True b) True c) False d) False e) True f) True g) False h) True i) False 6. When multiplying two single-term square root epressions, it s easiest to write the epression under one radical sign first. 7. Assuming all variables are nonnegative, the simplified answer for a problem that squares a square root or square roots a square is the radicand. In other words, squaring and square rooting are inverses not a real number z z. k k n p y p a m 8 6 7c d d 6y z y 8p q q 0 8 8a c d c 0 6 8v u v n m 7 y 0z 7 a 6 Section 9. Answers

4 Math :: Elementary Algebra c d d y y a 0 9z z 0mn 6 y yz ac 6 pq w k 9 6 a b 8 6 y z m 6c d Section 9. Answers

5 Math :: Elementary Algebra Section 9. Addition, Subtraction, and Multiplication of Radical Epressions. Only add square root epressions that have like-radicands. The eplanation should be in your own words.. This answer should be in your own words y y y 6a a a a a 9a 8. 6z z 6z 9. c c c 0. n n 7n Section 9. Answers

6 Math :: Elementary Algebra y y z z. n 9n n n w 6w 8. 8a 6a 9. z 60. This answer should be in your own words. Section 9. Answers

7 Math :: Elementary Algebra Section 9. Division of Radical Epressions. When simplifying a square root whose radicand is a quotient, usually it s easiest to simplify/reduce the fraction first, before taking the square root.. When simplifying an epression that consists of a quotient of square roots (without an addition or subtraction), simplify the fraction first.. The three conditions that must be met in order for a square root epression to be considered simplified are: a) No radicand can contain a factor that is a perfect square. b) The radicand is not a quotient. c) There are no radicals in the denominator.. This answer should be in your own words.. Epressions that require rationalizing the denominator are epressions with a single radical term in the denominator and epressions with two terms (at least one of which has a radical term). The net part of the answer should be in your own words m a.. 9 y.. z z w q p. m n y c d y y a a n c Section 9. Answers 6

8 Math :: Elementary Algebra 6. p p m m 6 9. z 0. 6 c c 8d y. y... p pq m 6n n a a 6y. y y y a a c a c y y y Section 9. Answers 7

9 Math :: Elementary Algebra Section 9. Simplifying Radical Epressions Part II. This answer should be in your own words.. This answer should be in your own words Section 9. Answers 8

10 Math :: Elementary Algebra Section 9.6 Radical Equations. a) b) c) d). The first part of this answer should be in your own words. The inverse of square rooting is squaring.. It is necessary to check your answers when solving a square root equation. The rest of this answer should be in your own words.. 6. y 6 6. a 8 7. m w 8 9. p 9 0. no solution; is an etraneous solution.. n. q 06. k. w. d 6. y k 9. no solution 0. a. p. n. no solution; is an etraneous solution.. 6; 9 is an etraneous solution.. k ; 7 is an etraneous solution. 6. w ; is an etraneous solution. 7. y ; 9 is an etraneous solution. 8. z ; 0 is an etraneous solution. 9. a 9 ; is an etraneous solution c ; is an etraneous solution. 9. m and 7. no solution; are etraneous solutions.. ; is an etraneous solution. Section 9.6 Answers 9

Radical Expressions and Graph (7.1) EXAMPLE #1: EXAMPLE #2: EXAMPLE #3: Find roots of numbers (Objective #1) Figure #1:

Radical Expressions and Graph (7.1) Find roots of numbers EXAMPLE #1: Figure #1: Find principal (positive) roots EXAMPLE #2: Find n th roots of n th powers (Objective #3) EXAMPLE #3: Figure #2: 7.1 Radical