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.
Arizona Academic Standards learning standard: 8.EE.A.2 · square roots and cube 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 Arizona
In the Arizona Academic Standards, 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.
Source: Arizona Department of Education
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 5²?
answer box
25
Hint: 5² means 5 × 5 = 25.
Question 2
What is √16?
answer box
4
Hint: Which number multiplied by itself makes 16? 4 × 4 = 16, so √16 = 4.
Question 3
Which of these numbers is a perfect square?
- 195
- 198
- 197
- 196
196
Hint: A perfect square is a whole number times itself. 14 × 14 = 196.
Question 4
√149 is between which two whole numbers?
- 10 and 11
- 12 and 13
- 11 and 12
- 13 and 14
12 and 13
Hint: 12² = 144 and 13² = 169. Since 149 is between them, √149 is between 12 and 13.
Question 5
A square floor tile has sides of 13 cm. What is its area?
answer boxcm²
169 cm²
Hint: Area of a square = side × side = 13 × 13 = 169 cm².
Question 6
√35 is closest to which whole number?
- 7
- 4
- 6
- 5
6
Hint: 5² = 25 and 36 = 6². 35 is closer to 36, so √35 is closest to 6.