Math 8:
1. Square and Cube Numbers
Name__________________________________________ Date: _____________________________ Blk______
1. Perfect squares can also be called square numbers.
72 represents 7 x 7 and can be read as “7 squared.”
Use your understanding of square numbers to fill in the missing parts in the next statement.
Perfect cubes can also be called ____________________. ____ represents 5 x 5 x 5 and can be read as “5 ________”
2. Which numbers are perfect squares? Show how you know.
a) 64
b) 120
c) 1000
d) 100
e) 900
f) 10 000
e) 800
f) 10 000
3. Which numbers are perfect cubes? Show how you know.
a) 64
b) 125
c) 1000
d) 100
4. Barrett is making a display of 225 square photos of the students in his school. Each photo is the same size. Can he
arrange the photos in a square? Explain.
5. Barrett is making a giant Rubik cube display using 216 smaller Rubik cubes. Each cube is the same size. Can he
arrange the smaller cubes into a larger cube? Explain.
6. Calculate.
a) 62
b) 122
c) 10002
d) 43
e) 803
f) 1003
g) (– 6)2
h) (– 3)2
i) – (5)2
j) (– 2)3
k) (– 1)3
l) – (– 3)3
7. Guy says: “My street address is a square number when you read the digits forward or backward.” Is Guy correct?
Explain.
8. a) How many perfect squares are between 900 and 1000? Show your work.
b) How can you use your answers in part (a) to determine the greatest perfect square less than 900 and the least
perfect square greater than 1000?
9. a) How many perfect cubes are between 300 and 600? Show your work.
b) How can you use your answers in part (a) to determine the greatest perfect cube less than 300 and the least perfect
cube greater than 600?
10. Are 0 and 1 both square and cube numbers? Explain.
11. a) When you square a number, how do you know whether the result will be odd or even?
b) When you cube a number, how do you know whether the result will be odd or even?
12. I can determine whether 441 is a perfect square using prime factors (Factor tree).
Rearranging the prime factors into two equal groups creates a pair of equal factors
441 = 3 × 3 × 7 × 7 = (3 × 7) × (3 × 7)
13. Determine if each of the following numbers are square numbers using prime factors.
a) 324
b) 2800
c) 1156
Complete a factor tree for 3375
14. I can determine whether 3375 is a perfect cube using prime factors (Factor tree).
Rearranging the prime factors into three equal groups creates three equal factors
3375 =
=(
)×(
)×(
)
15. Determine if each of the following numbers are cube numbers using prime factors.
a) 864
b) 1728
c) 5832
16. Tom says “if you square or cube a number the answer is always bigger.” A counter example proves a rule wrong.
Show Tom he is incorrect by providing counter examples. Explain why your counter examples produce a smaller
answer.
17. a) James says the sum of the first two cube numbers is a square number. Is he correct?
b) What about the first three cube numbers?
c) What about the first four cube numbers?
18. A classroom has a box with 800 linking cubes in it. What is the side length of the largest solid cube the class can build
with these linking cubes?
19. a) 75 is not a square number. Which two consecutive square numbers is 75 between?
b) 200 is not a cube number. Which two consecutive cube numbers is 200 between?