Math Grade 6-8

Math: Square Roots and Cube Roots

Finding roots and connecting them to powers

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Finding roots and connecting them to powers

Math - Grade 6-8

Instructions: Read each problem carefully. Show your work in the space provided. Use exact answers when possible, and estimate when asked.
  1. 1
    A square grid of small tiles showing a nine by nine array.

    Find the square root of 81. Explain how you know.

  2. 2
    A cube made of smaller unit cubes with four cubes along each edge.

    Find the cube root of 64. Explain how you know.

  3. 3
    A square area model divided into seven rows and seven columns.

    A square has an area of 49 square centimeters. What is the side length of the square?

  4. 4
    A cube made of smaller unit cubes with five cubes along each edge.

    A cube has a volume of 125 cubic inches. What is the length of one edge of the cube?

  5. 5

    List all the perfect squares between 1 and 100, including 1 and 100.

  6. 6

    List all the perfect cubes between 1 and 125, including 1 and 125.

  7. 7
    A square grid of tiles showing a twelve by twelve array.

    Simplify: √144

  8. 8
    A cube made of smaller unit cubes with six cubes along each edge.

    Simplify: ∛216

  9. 9
    Two square grids compare a smaller and larger square with a tile cluster between them.

    Estimate √50 to the nearest whole number. Explain your reasoning.

  10. 10
    Two cube models compare a smaller and larger cube with a loose stack of unit cubes between them.

    Estimate ∛30 to the nearest whole number. Explain your reasoning.

  11. 11
    Three increasing square tile arrays with the side of the largest square highlighted.

    Complete the pattern: 2 squared = 4, 3 squared = 9, 4 squared = 16, so √16 = ___. Explain the relationship.

  12. 12
    A square tile array is contrasted with two straight rows of tiles.

    A student says that √36 equals 18 because 18 plus 18 equals 36. Explain the mistake and give the correct answer.

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