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8th grade · Math · Unit 1 of 11

Squares, Cubes & Roots

Perfect squares and cubes, and their roots

What your child practices

Knowing perfect squares and cubes, finding square roots and cube roots, estimating where a square root falls between whole numbers, and linking squares to the area of a square.

Minnesota K-12 Academic Standards benchmark: 8.3.6.4; 8.3.5.1 · squares and square roots, and rational and irrational numbers

How we explain it

Children can open this short lesson before they practice.

  1. A square number is a number times itself: 3² = 3 × 3 = 9.
  2. A square root undoes a square: √81 = 9.
  3. A cube is a number multiplied 3 times: 2³ = 2 × 2 × 2 = 8.

Example: What is √81 + 3²? √81 = 9, because 9 × 9 = 81. 3² = 9. 9 + 9 = 18. Answer: 18

Squares, Cubes & Roots in Minnesota

In the Minnesota K-12 Academic Standards, this is unit 1 of 11 in 8th grade Math, before Patterns & Two-Step Equations.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Minnesota Department of Education (MDE)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    What is 8²?

    answer box

  2. Question 2

    What is √196?

    answer box

  3. Question 3

    Which of these numbers is a perfect square?

    • 101
    • 99
    • 102
    • 100

  4. Question 4

    √87 is between which two whole numbers?

    • 8 and 9
    • 7 and 8
    • 10 and 11
    • 9 and 10

  5. Question 5

    Mei's square garden has an area of 16 m². How long is each side?

    answer boxm

  6. Question 6

    √99 is closest to which whole number?

    • 8
    • 10
    • 9
    • 11

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