Integer powers and roots

Mathematics · Number Representation & Place Value · ages 11-14

Name ______________________ Date ____________

Which of these numbers is a perfect square?
- 45
- 49
- 52
- 60
How many perfect square numbers are there from 1 to 100?
Answer: ______________
What is 6²?
- 12
- 36
- 64
True or false: 5² means 5 × 2.
Circle one: True False
Which power of 2 equals 32?
- 2⁴
- 2⁵
- 2⁶
Which whole number is the closest approximation to √50?
- 6
- 7
- 8
- 9
How many whole numbers between 101 and 1000 are perfect squares?
Answer: ______________
What is ∛64?
- 4
- 8
- 6
Mia says √50 equals exactly 7. What's wrong with her answer?
- 50 is an even number, so it cannot have a square root
- She should have said 8 instead of 7
- 7² = 49, not 50, so √50 is a little more than 7
√90 sits between two whole numbers. Type the smaller one.
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

49 · 49 = 7×7, so it's a perfect square. The others aren't the product of a whole number multiplied by itself.
10 · The perfect squares from 1 to 100 are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. That's 10 numbers.
36 · 6² means 6 × 6, which is 36. Doubling 6 gives 12, and that's a common mix-up.
False · The small 2 means 5 × 5, using 5 twice in a multiplication. 5 × 2 would just double it.
2⁵ · The powers of 2 go 2, 4, 8, 16, 32, so 2⁵ = 32.
7 · 7²=49 and 8²=64. Since 50 is very close to 49, √50 ≈ 7.07, so 7 is the closest whole number.
21 · The perfect squares in this range run from 11²=121 up to 31²=961, which is 21 numbers.
4 · 4 × 4 × 4 = 64, so the cube root of 64 is 4. 8 is close because 8² = 64, but that's a square, not a cube.
7² = 49, not 50, so √50 is a little more than 7 · Since 7² = 49 and 8² = 64, 50 sits between them, so √50 is close to 7 but not exact.
9 · 9² = 81 and 10² = 100. Since 90 is between them, √90 is between 9 and 10.