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8th grade · Math · Unit 1 of 19

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.

New York State Learning Standards learning standard: NY-8.EE.2 · square roots of perfect squares and cube roots of perfect cubes

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 New York

In the New York State Learning Standards, this is unit 1 of 19 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: New York State Education Department (NYSED)

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 5²?

    answer box

  2. Question 2

    What is √36?

    answer box

  3. Question 3

    Which of these numbers is a perfect square?

    • 171
    • 168
    • 170
    • 169

  4. Question 4

    √164 is between which two whole numbers?

    • 10 and 11
    • 12 and 13
    • 11 and 12
    • 13 and 14

  5. Question 5

    A square floor tile has sides of 11 cm. What is its area?

    answer boxcm²

  6. Question 6

    √48 is closest to which whole number?

    • 6
    • 7
    • 8
    • 5

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