Grade 9 · Math · Unit 3 of 9
Square Roots
Perfect squares and good estimates
What your child practises
Finding the square root of whole numbers, decimals and fractions that are perfect squares, and estimating the square root of other numbers by placing them between two perfect squares.
Nunavut Curriculum approved guide: Alberta Mathematics K–9 (2007), Number · square roots of perfect squares, and estimating square roots that are not perfect squares
How we explain it
Children can open this short lesson before they practise.
- A square root undoes squaring: the square root of 81 is 9.
- A perfect square has a whole-number square root.
- Estimate between the two nearest perfect squares.
Example: Estimate the square root of 50. 49 = 7² and 64 = 8². 50 is just above 49. Answer: About 7.1
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
A square garden has an area of 64 m². How long is one side, in metres?
answer boxm
8 m
Hint: The area of a square is side × side. Find the number that multiplies by itself to give 64: 8 × 8.
Question 2
Which is greater, √359 or 19?
- They are equal
- 19
- √359
19
Hint: 19² = 361. 359 is less than 361, so √359 is less than 19.
Question 3
What is √0.81?
answer box
0.9
Hint: 0.9 × 0.9 = 0.81. A decimal with 2 places has a square root with 1 place.
Question 4
Which number is a perfect square?
- 262
- 257
- 259
- 256
256
Hint: A perfect square is a whole number times itself. 16 × 16 = 256.
Question 5
√13 is between which two whole numbers?
- 1 and 2
- 4 and 5
- 3 and 4
- 2 and 3
3 and 4
Hint: 3² = 9 and 4² = 16. Since 13 is between 9 and 16, its square root is between 3 and 4.
Question 6
Which whole number is closest to √364?
- 19
- 20
- 18
- 21
19
Hint: Find the perfect squares on each side of 364. 19² = 361, which is the closest to 364.