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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. The distinction between the principal square root of the number x and the secondary square root of the number x is made by explanation and by example. The simplification of the radical expressions that both involve and do not involve fractions is shown in many detailed examples; this is followed by an explanation of how and why radicals are eliminated from the denominator of a radical expression. Real-life applications of radical equations have been included, such as problems involving daily output, daily sales, electronic resonance frequency, and kinetic energy.This module contains an exercise supplement for the chapter "Roots, Radicals, and Square Root Equations".

Exercise supplement

Square root expressions ( [link] ) - addition and subtraction of square root expressions ( [link] )

For the following problems, simplify the expressions.

x + 5 x + 2

( x + 5 ) ( x + 2 ) x + 2

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a 2 + 6 a + 9 a + 3

a + 3

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x 2 11 x + 24 x 8

x 3

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a ( a b c )

a a b c

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7 a 3 ( 2 a 4 a 3 )

a 2 14 2 a 3 7

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( 4 y 3 x ) ( 4 y + 3 x )

16 y 2 3 x

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( 6 r + 2 s ) ( 4 r + 2 s )

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2 2 + 7

2 ( 2 7 ) 3

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6 x + y

6 ( x y ) x 2 y

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5 a + 3

a 5 15 a 2 3

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8 + 3 2 + 6

8 6 2 3 + 3 2 16 2

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36 a 4 b 5 c 11 x 2 y 5

6 a 2 b 2 c 5 b c y x y 3

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32 x 5 y ( x 2 ) 3

4 x 2 ( x 2 ) 2 x y ( x 2 )

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( x + 4 ) 4 ( x 1 ) 5

( x + 4 ) 2 ( x 1 ) 2 ( x 1 )

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( 3 x + 5 ) 3 ( 2 x 7 ) 3

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( y 3 z ) 12 ( y + 3 z ) 10 ( y 5 z ) 3

( y 3 z ) 6 ( y + 3 z ) 5 ( y 5 z ) y 5 z

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( 8 a 5 b ) 26 ( 2 a 9 b ) 40 ( a b ) 15

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4 a x 2 75 x 4 + 6 a 3 x 8

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3 54 16 96

73 6

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4 x 2 + 32 x + 64 + 10 x 2 + 80 x + 160

( 2 + 10 ) ( x + 4 )

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2 9 x 2 42 x + 49 + 5 18 x 2 84 x + 98

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10 56 a 3 b 7 + 2 a 2 b 126 a b 5

( 20 a b 3 + 6 a 2 b 3 ) 14 a b

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6 a + 2 a 3 a 5 a

3 2 30 6 10 2

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Square root equations with applications ( [link] )

For the following problems, solve the equations.

a + 6 = 5

no solution

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5 b + 4 5 = 2

b = 1

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2 x + 5 = x + 3

x = 2

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At a small business, the monthly number of sales S is approximately related to the number of employees E by S = 140 + 8 E 2 .

(a) Determine the approximate number of sales if the number of employees is 27.

(b) Determine the approximate number of employees if the monthly sales are 268.

( a ) S = 180 ; ( b ) E = 258

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The resonance frequency f in an electronic circuit containing inductance L and capacitance C in series is given by

f = 1 2 π L C

(a) Determine the resonance frequency in an electronic circuit if the inductance is 9 and the capacitance is 0.0001 . Use π = 3.14.

(b) Determine the inductance in an electric circuit if the resonance frequency is 5.308 and the capacitance is 0.0001 . Use π = 3.14.

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If two magnetic poles of strength m and m ' units are at a distance r centimeters (cm) apart, the force F of repulsion in air between them is given by

F = m m ' r 2

(a) Determine the force of repulsion if two magnetic poles of strengths 22 and 46 units are 8 cm apart.

(b) Determine how far apart are two magnetic poles of strengths 14 and 16 units if the force of repulsion in air between them is 42 units.

( a ) F = 15.8125 ( b ) r = 12.31 cm

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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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