Multiplying, dividing and mixed operations · Ages 9–10

Square and cube numbers worksheet

Part of: Multiplying and dividing by two digits; divisibility

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Multiplying, dividing and mixed operations · Ages 9–10

Numsprite
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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

13.Ka-lok has built a cube 2 small cubes along each edge and wants to make it 3 along each edge. How many more small cubes are needed?
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14.A square balcony is covered exactly by square tiles, 13 along each side. How many tiles cover it?
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15.Ka-yee builds a big cube from small cubes, 5 along each edge. How many small cubes does Ka-yee use?
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16.Tsz-ching uses exactly 64 small cubes to build one big cube. How many small cubes are along each edge?
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17.A storeroom has 9 crates of mooncakes, 9 boxes in each crate and 9 mooncakes in each box. How many mooncakes are there?
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18.A square balcony is covered exactly by square tiles, 5 along each side. How many tiles cover it?
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Show the answers and working

Square and cube numbers worksheet: Answers and working

1. 125
5³ is three 5s multiplied: work out 5 × 5 first, then times 5 once more.
5³ is three 5s multiplied: 5 × 5 = 25, then 25 × 5 = 125.
2. 4
2² means two 2s multiplied, not 2 × 2.
2² is two 2s multiplied: 2 × 2 = 4.
3. 8
2³ is three 2s multiplied: work out 2 × 2 first, then times 2 once more.
2³ is three 2s multiplied: 2 × 2 = 4, then 4 × 2 = 8.
4. 5
□ times itself makes 25. Think through the times tables: which number times itself gives 25?
Find the number that times itself makes 25: 5 × 5 = 25.
5. 81, 729
Find 9² first, that is 9 × 9; then multiply the result by 9.
Square first: 9² = 9 × 9 = 81; then once more: 81 × 9 = 729.
6. 25, 125
Find 5² first, that is 5 × 5; then multiply the result by 5.
Square first: 5² = 5 × 5 = 25; then once more: 25 × 5 = 125.
7. 27
Work out the cube numbers in turn, 1 × 1 × 1, 2 × 2 × 2, …, until you pass 60.
The cube numbers go 1, 8, 27, 64, 125, 216…: the largest below 60 is 27.
8. 8
Work out the cube numbers in turn, 1 × 1 × 1, 2 × 2 × 2, …, until you pass 14.
The cube numbers go 1, 8, 27, 64, 125, 216…: the largest below 14 is 8.

9. C. 9 × 9
What does the small raised 2 mean: adding, multiplying the number by itself, or times 2?
9² is read “9 squared”: two 9s multiplied, 9 × 9.
10. False
2³ is three 2s multiplied, not 2 × 3. Work out 2 × 2, times 2, then compare with 4.
2³ = 2 × 2 × 2 = 8.
11. A. 64
A cube number is three equal numbers multiplied. Try 2 × 2 × 2, 3 × 3 × 3, … and compare with each choice.
64 = 4 × 4 × 4 = 4³: a cube number.
12. True
2³ is three 2s multiplied, not 2 × 3. Work out 2 × 2, times 2, then compare with 8.
2³ = 2 × 2 × 2 = 8.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 19 cubes
First work out how many small cubes each cube takes: 2³ and 3³.
3³ − 2³ = 27 − 8 = 19.
14. 169 tiles
The balcony has 13 rows of 13 tiles: that is 13².
13 rows of 13: 13² = 13 × 13 = 169.
15. 125 cubes
First work out one layer: 5 × 5; the big cube has 5 layers.
5 × 5 = 25 a layer, 5 layers: 5³ = 125.
16. 4 cubes
Find the number that, three of it multiplied, makes exactly 64. Try small numbers in turn.
Find the number that, three of it multiplied, makes 64: 4 × 4 × 4 = 64, so 4³ = 64.
17. 729 mooncakes
First work out one crate: 9 boxes of 9; then multiply by the number of crates.
9 × 9 × 9 = 9³: 81 a crate, 729 in 9 crates.
18. 25 tiles
The balcony has 5 rows of 5 tiles: that is 5².
5 rows of 5: 5² = 5 × 5 = 25.

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