← Back to Topic 6

Solving x² = p and x³ = p: Classroom Packet

Grade 8 Algebra: Solving x² = p and x³ = p

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Perfect squares and cubes

  1. 1. Solve:
    x2=36x^2=36
  2. 2. Solve:
    x2=81x^2=81
  3. 3. Solve:
    x3=8x^3=8
  4. 4. Solve:
    x3=125x^3=125
  5. 5. Solve:
    x2=144x^2=144
  6. 6. Solve:
    x3=−27x^3=-27
  7. 7. Solve:
    x2=1x^2=1
  8. 8. Solve:
    x3=1000x^3=1000

Answer Key

Level 1

  1. 1. x=±6x=\pm 6
  2. 2. x=±9x=\pm 9
  3. 3. x=2x=2
  4. 4. x=5x=5
  5. 5. x=±12x=\pm 12
  6. 6. x=−3x=-3
  7. 7. x=±1x=\pm 1
  8. 8. x=10x=10

Grade 8 Algebra: Solving x² = p and x³ = p

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Rearrange first

  1. 1. Solve:
    x2+5=30x^2+5=30
  2. 2. Solve:
    2x2=502x^2=50
  3. 3. Solve:
    x3−4=60x^3-4=60
  4. 4. Solve:
    3x3=243x^3=24
  5. 5. Solve:
    x2−7=42x^2-7=42
  6. 6. Solve:
    x22=32\tfrac{x^2}{2}=32
  7. 7. Solve:
    x3+10=−54x^3+10=-54
  8. 8. Solve:
    4x2−1=994x^2-1=99

Answer Key

Level 2

  1. 1. x=±5x=\pm 5
  2. 2. x=±5x=\pm 5
  3. 3. x=4x=4
  4. 4. x=2x=2
  5. 5. x=±7x=\pm 7
  6. 6. x=±8x=\pm 8
  7. 7. x=−4x=-4
  8. 8. x=±5x=\pm 5

Grade 8 Algebra: Solving x² = p and x³ = p

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Fractions and irrational answers

  1. 1. Solve:
    x2=925x^2=\tfrac{9}{25}
  2. 2. Solve:
    x3=164x^3=\tfrac{1}{64}
  3. 3. Solve:
    x2=7x^2=7
  4. 4. Solve:
    x3=10x^3=10
  5. 5. Solve:
    x2=0.16x^2=0.16
  6. 6. Solve:
    5x2=155x^2=15
  7. 7. Solve:
    x3=−8125x^3=-\tfrac{8}{125}
  8. 8. Solve:
    2x3+3=192x^3+3=19

Answer Key

Level 3

  1. 1. x=±35x=\pm\tfrac{3}{5}
  2. 2. x=14x=\tfrac{1}{4}
  3. 3. x=±7x=\pm\sqrt{7}
  4. 4. x=103x=\sqrt[3]{10}
  5. 5. x=±0.4x=\pm 0.4
  6. 6. x=±3x=\pm\sqrt{3}
  7. 7. x=−25x=-\tfrac{2}{5}
  8. 8. x=2x=2