Skip to content Skip to navigation Skip to collection information

Connexions

You are here: Home » Content » Elementary Algebra » Proficiency Exam

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Endorsed by Endorsed (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
  • College Open Textbooks display tagshide tags

    This collection is included inLens: Community College Open Textbook Collaborative
    By: CC Open Textbook Collaborative

    Comments:

    "Reviewer's Comments: 'I recommend this book for courses in elementary algebra. The chapters are fairly clear and comprehensible, making them quite readable. The authors do a particularly nice job […]"

    Click the "College Open Textbooks" link to see all content they endorse.

    Click the tag icon tag icon to display tags associated with this content.

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • OrangeGrove display tagshide tags

    This collection is included inLens: Florida Orange Grove Textbooks
    By: Florida Orange Grove

    Click the "OrangeGrove" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

  • Featured Content display tagshide tags

    This collection is included inLens: Connexions Featured Content
    By: Connexions

    Comments:

    "Elementary Algebra covers traditional topics studied in a modern elementary algebra course. Written by Denny Burzynski and Wade Ellis, it is intended for both first-time students and those […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Proficiency Exam

Module by: Wade Ellis, Denny Burzynski. E-mail the authors

Summary: 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 the proficiency exam for the chapter "Roots, Radicals, and Square Root Equations".

Proficiency Exam

For the following problems, simplify each of the square root expressions.

Exercise 1

((Reference)) 8 · 5 8 · 5

Solution

2 10 2 10

Exercise 2

((Reference)) 80 12 80 12

Solution

2 15 3 2 15 3

Exercise 3

((Reference), (Reference)) n 2 +n-12 n-3 n 2 +n-12 n-3

Solution

n+4 n+4

Exercise 4

((Reference), (Reference)) 24 a 3 b 5 c 8 24 a 3 b 5 c 8

Solution

2a b 2 c 4 6ab 2a b 2 c 4 6ab

Exercise 5

((Reference), (Reference)) 64 x 4 y 5 z 6 49 a 3 b 2 c 9 64 x 4 y 5 z 6 49 a 3 b 2 c 9

Solution

8 x 2 y 2 z 3 acy 7 a 2 b c 5 8 x 2 y 2 z 3 acy 7 a 2 b c 5

Exercise 6

((Reference)) ( x-2 ) 2 ( x+1 ) 4 ( x-2 ) 2 ( x+1 ) 4

Solution

( x−2 ) ( x+1 ) 2 ( x−2 ) ( x+1 ) 2

Exercise 7

((Reference)) a 2 -8a+16 a 2 -8a+16

Solution

a−4 a−4

Exercise 8

((Reference)) 4 2+ x 4 2+ x

Solution

8−4 x 4−x 8−4 x 4−x

Exercise 9

((Reference) 3a 2a + 5a 3a 2a + 5a

Solution

15 − 6 3 15 − 6 3

Exercise 10

((Reference) 2x 27 +x 12 2x 27 +x 12

Solution

8x 3 8x 3

Exercise 11

((Reference)) -3a a 5 b 3 +2 a 3 b ab -3a a 5 b 3 +2 a 3 b ab

Solution

− a 3 b ab − a 3 b ab

Exercise 12

((Reference), (Reference)) 10 ( 8 - 2 ) 10 ( 8 - 2 )

Solution

2 5 2 5

Exercise 13

((Reference), (Reference)) ( 3+ 6 )( 2+ 5 ) ( 3+ 6 )( 2+ 5 )

Solution

6+3 5 +2 6 + 30 6+3 5 +2 6 + 30

Exercise 14

((Reference), (Reference)) ( 10 - 3 )( 5 + 2 ) ( 10 - 3 )( 5 + 2 )

Solution

5 2 +2 5 − 15 − 6 5 2 +2 5 − 15 − 6

Exercise 15

((Reference), (Reference)) ( 4- 5y ) 2 ( 4- 5y ) 2

Solution

16−8 5y +5y 16−8 5y +5y

Exercise 16

((Reference), (Reference)) 6- 3 4+ 2 6- 3 4+ 2

Solution

24−6 2 −4 3 + 6 14 24−6 2 −4 3 + 6 14

Exercise 17

((Reference), (Reference)) 2 + 3 3 - 5 2 + 3 3 - 5

Solution

− 3+ 6 + 10 + 15 2 − 3+ 6 + 10 + 15 2

For the following problems, solve the equations.

Exercise 18

((Reference)) x+8 =4 x+8 =4

Solution

x=8 x=8

Exercise 19

((Reference)) 3a+1 =4 3a+1 =4

Solution

a=5 a=5

Exercise 20

((Reference)) 2x =-3 2x =-3

Solution

no solution

Exercise 21

((Reference)) 3x+18 +7=0 3x+18 +7=0

Solution

no real solution

Exercise 22

((Reference)) 3m-5 = 2m+1 3m-5 = 2m+1

Solution

m=6 m=6

Exercise 23

((Reference)) 2 a+2 −2=0 2 a+2 −2=0

Solution

a=−1 a=−1

Exercise 24

((Reference)) b-7 - 5b+1 =0 b-7 - 5b+1 =0

Solution

no solution

Exercise 25

((Reference)) At a small business, the number of monthly sales S S is approximately related to the number of employees E E by S=175+7 E−3 . S=175+7 E−3 .

(a) Determine the approximate number of sales if the number of employees is 39.
(b) Determine the approximate number of employees if the number of sales is 224.

Solution

(a) S=217 S=217 (b) E=52 E=52

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks