8th grade · Math · Unit 1 of 17
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.
Alabama Course of Study content standard: 8.2; 8.4 · square roots and cube roots, and estimating square roots
How we explain it
Children can open this short lesson before they practice.
- A square number is a number times itself: 3² = 3 × 3 = 9.
- A square root undoes a square: √81 = 9.
- 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 Alabama
In the Alabama Course of Study, this is unit 1 of 17 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.
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
What is 9²?
answer box
81
Hint: 9² means 9 × 9 = 81.
Question 2
What is √121?
answer box
11
Hint: Which number multiplied by itself makes 121? 11 × 11 = 121, so √121 = 11.
Question 3
Which of these numbers is a perfect square?
- 100
- 101
- 99
- 102
100
Hint: A perfect square is a whole number times itself. 10 × 10 = 100.
Question 4
√67 is between which two whole numbers?
- 8 and 9
- 6 and 7
- 7 and 8
- 9 and 10
8 and 9
Hint: 8² = 64 and 9² = 81. Since 67 is between them, √67 is between 8 and 9.
Question 5
Leo's square garden has an area of 36 m². How long is each side?
answer boxm
6 m
Hint: The area of a square is side × side, so the side is √36 = 6 m.
Question 6
√83 is closest to which whole number?
- 8
- 9
- 10
- 11
9
Hint: 9² = 81 and 100 = 10². 83 is closer to 81, so √83 is closest to 9.