Grade 8 · Math · Unit 2 of 18
Squares, Cubes & Roots
Perfect squares and cubes, and their roots
What your child practises
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.
Ontario Curriculum expectation: B1.3, B2.2 · square numbers, square roots and estimating square roots
How we explain it
Children can open this short lesson before they practise.
- 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
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 10²?
answer box
Show answer
100
Hint: 10² means 10 × 10 = 100.
Question 2
What is √36?
answer box
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6
Hint: Which number multiplied by itself makes 36? 6 × 6 = 36, so √36 = 6.
Question 3
Which of these numbers is a perfect square?
- 80
- 82
- 83
- 81
Show answer
81
Hint: A perfect square is a whole number times itself. 9 × 9 = 81.
Question 4
√77 is between which two whole numbers?
- 8 and 9
- 9 and 10
- 7 and 8
- 6 and 7
Show answer
8 and 9
Hint: 8² = 64 and 9² = 81. Since 77 is between them, √77 is between 8 and 9.
Question 5
Omar's square garden has an area of 169 m². How long is each side?
answer boxm
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13 m
Hint: The area of a square is side × side, so the side is √169 = 13 m.
Question 6
√126 is closest to which whole number?
- 12
- 10
- 13
- 11
Show answer
11
Hint: 11² = 121 and 144 = 12². 126 is closer to 121, so √126 is closest to 11.