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8th grade · Math · Unit 2 of 15

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.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: 8.2(B) · square roots and estimating 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 Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 2 of 15 in 8th grade Math, after Big, Small & Real Numbers and before Tessellations & Transformations.

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: Texas Education Agency (TEA)

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 3²?

    answer box

  2. Question 2

    What is √121?

    answer box

  3. Question 3

    Which of these numbers is a perfect square?

    • 48
    • 50
    • 51
    • 49

  4. Question 4

    √127 is between which two whole numbers?

    • 12 and 13
    • 11 and 12
    • 9 and 10
    • 10 and 11

  5. Question 5

    A square floor tile has sides of 10 cm. What is its area?

    answer boxcm²

  6. Question 6

    √34 is closest to which whole number?

    • 4
    • 7
    • 6
    • 5

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