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Algebra - Mixed Practice (Up to Radical Expressions)

Lesson Plans > Mathematics > Algebra > Mixed Content
 

Algebra - Mixed Practice (Up to Radical Expressions)

This section has three worksheets. The first two include simplifying radical expressions and the third includes solving radical equations. 

In the first worksheet, all radical expressions have radicals only in the numerator. In the second worksheet, there will also be radicals in the denominator, and are simplified by multiplying numerator and denominator by the conjugate of the denominator.

In the final worksheet, most of the problems involve squaring each side just once. The final three problems require squaring twice.

Worksheet 9.1

  • Writing algebraic expressions
  • Solving linear equations
  • Simplifying radical expressions

Worksheet 9.2

  • Simplifying complex fractions
  • Multiplying difference of squares
  • Simplifying radical expressions

Worksheet 9.3

  • Squaring binomials
  • Writing and simplifying radical expressions
  • Solving radical equations

Worksheet Sets in this Series

Worksheets for this section are below the index. Click the "Overview" link to get a more detailed view of the entire series.

Lesson by Mr. Twitchell

Handouts/Worksheets

Mixed Practice 9.1

Write algebraic expressions

  1. The sum of a number and its square root
     
  2. The square root of five less than twice a number
     
  3. A third of the square root of a number
     
  4. Two more than a number, times the square root of seven less than the number
     
  5. The product of half a number with the square root of ten times the sum of seven and the number squared

    Solve the following linear equations
     
  6. 3x + 20 = 12
     
  7. 2(x - 5) = 24
     
  8. 3x + 2(-x + 5) = 30
     
  9. 2x(x + 7) = x(2x - 10) + 4(x + 2)
     
  10. (5x + 1) - (4x - 1) + (3x + 1) - (2x - 1) + (x + 1) = 18

    Simplify the radical expressions
     
  11. 96

     
  12. 240

     
  13. 98

     
  14. 32
    +
    128

     
  15. 10
    90
    + 5
    810

     
  16. 3
    +
    5
    +
    27
    +
    45

     
  17. 2
    3
    54
    -
    1
    2
    24

     
  18. 10
    (
    40
    -
    10
    +
    90
    )
     
  19. 3
    2
    (
    2
    +
    3
    +
    8
    )
     
  20. 14 + 10
    14 - 10

Mixed Practice 9.1: Answer Key

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Mixed Practice 9.2

Simplify the following expressions

  1. a2
    b
    c
    b

     
  2. x + 2
    2x + 4
    2x

     
  3. x + 1
    x - 1
    x2 - 1
    x - 1

     
  4. 1 +
    1
    x
    1 -
    1
    x

     
  5. (x - 2)(x + 2) = 
     
  6. (3x - 4)(3x + 4)  =
     
  7. (
    1
    2
    x +
    y
    3
    )(
    1
    2
    x -
    y
    3
    ) =
     
  8. (2 +
    2
    )(2 -
    2
    ) = 
     
  9. (5 -
    3
    )(5 +
    3
    ) = 
     
  10. (7 + 3
    5
    )(7 - 3
    5
    ) = 
     
  11. 5
    2
    =
     
  12. 3
    3 -
    3
    =
     
  13. 1 +
    2
    1 -
    2

     
  14. 10
    7
    -
    2

     
  15. 1 +
    3
    12
    + 1

Mixed Practice 9.2: Answer Key

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Mixed Practice 9.3

Simplify the following expressions

  1. (x + 3)2
     
  2. (x - 5)2
     
  3. (2x - 3)2 =
     
  4. (x +
    3
    )2
     
  5. (
    3
    -
    2
    )2
     
  6. The product of one less than the square root of a number with one more than the square root of that number
     
  7. The square of the sum of one and the square root of a number
     
  8. Half of a number times the square root of 4 less than four times the number
     
  9. Seven divided by the difference between the square root of ten and the square root of three
     
  10. The reciprocal of three more than the square root of seven

    Solve the following radical equations
     
  11. x
    = 2
    7

     
  12. 5 +
    x
    = 10
     
  13. x
    = x - 6
     
  14. x - 1
    =
    4x - 13

     
  15. 3
    x
    - 1
    =
    1
    3

     
  16. x
    +
    x - 5
    = 5
     
  17. x - 6
    -
    x + 7
    = -1
     
  18. 6 -
    x
    =
    x - 12

Mixed Practice 9.3: Answer Key

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