Cubes and cube roots

The Maths Habit

How many small squares?

2 × 2 = 4
3 × 3 = 9
4 × 4 = 16

Which of these are cubes? How do you know?

ACube
BNot a cube
CCube
DNot a cube

A cube has the same number along, up and back.

edge
Edge
Where two faces of a cube meet.
edgeedgeedge
Cubed
A number multiplied by itself, then by itself again. The small ³ means cubed.
Cube number
The answer when a whole number is cubed.
cubesedgeedgeedge
Cube root
The number that was cubed. The sign is ∛.

This cube comes apart in layers.

  1. How many small cubes in one layer?3 × 3 = 9
  2. How many layers?3
  3. How many small cubes altogether?9 × 3 = 27

edgeedgeedgecubes
edge×edge×edge
=layer×edge=cubes
edge3=cubes
  1. 1Label the cube.Write the edge on three edges.
  2. 2Edge × edge × edge.One layer is edge × edge. Times it by the edge for all the layers. The small ³ does not mean × 3.
  3. 3Write the answer.It is the number of small cubes. It is a cube number.

Work out 43.

1Label the cube.
44464?
2Edge × edge × edge.
4×4×4
=16×4=64
3Write the answer.
43 =64

Work out 23.

1Label the cube.
2228?
2Edge × edge × edge.
2×2×2
=4×2=8
3Write the answer.
23 =8

Work out 43.

1Label the cube.
44464?
2Edge × edge × edge.
4×4×4
=16×4=64
3Write the answer.
43 =64
1edgeedgeedge2edge×edge×edge=layer×edge=cubes3edge3=cubes

Work out 103.

1Label the cube.
1010101000?
2Edge × edge × edge.
10×10×10
=100×10=1000
3Write the answer.
103 =1000

Work out 43.

1Label the cube.
44464?
2Edge × edge × edge.
4×4×4
=16×4=64
3Write the answer.
43 =64
1edgeedgeedge2edge×edge×edge=layer×edge=cubes3edge3=cubes

Work out 53.

1Label the cube.
555125?
2Edge × edge × edge.
5×5×5
=25×5=125
3Write the answer.
53 =125

Work out 43.

1Label the cube.
44464?
2Edge × edge × edge.
4×4×4
=16×4=64
3Write the answer.
43 =64
1edgeedgeedge2edge×edge×edge=layer×edge=cubes3edge3=cubes

Work out 33.

1Label the cube.
33327?
2Edge × edge × edge.
3×3×3
=9×3=27
3Write the answer.
33 =27

1edgeedgeedge2edge×edge×edge=layer×edge=cubes3edge3=cubes

1Work out 13.

1
1111?
2
1×1×1
=1×1=1
3
13 =1

2A big cube has 4 small cubes along each edge. How many small cubes make the big cube?

1
44464?
2
4×4×4
=16×4=64
3
Small cubes =64

3Work out 53.

1
555125?
2
5×5×5
=25×5=125
3
53 =125

Copy and finish the cube numbers.

Edge1234510Edge × edge × edge1827641251000

cubesedgeedgeedge
edge×edge×edge
=layer×edge=cubes
∛cubes=edge
  1. 1Label the cube.Write the number of small cubes on the front.
  2. 2Edge × edge × edge.Which number, three times, makes it? Try one and check.
  3. 3Write the answer.The edge is the cube root.

Work out ∛27.

1Label the cube.
27?3?3?3
2Edge × edge × edge.
3×3×3
=9×3=27
3Write the answer.
∛27 =3

Work out ∛8.

1Label the cube.
8?2?2?2
2Edge × edge × edge.
2×2×2
=4×2=8
3Write the answer.
∛8 =2

Work out ∛27.

1Label the cube.
27?3?3?3
2Edge × edge × edge.
3×3×3
=9×3=27
3Write the answer.
∛27 =3
1cubesedgeedgeedge2edge×edge×edge=layer×edge=cubes3∛cubes=edge

Work out ∛1000.

1Label the cube.
1000?10?10?10
2Edge × edge × edge.
10×10×10
=100×10=1000
3Write the answer.
∛1000 =10

Work out ∛27.

1Label the cube.
27?3?3?3
2Edge × edge × edge.
3×3×3
=9×3=27
3Write the answer.
∛27 =3
1cubesedgeedgeedge2edge×edge×edge=layer×edge=cubes3∛cubes=edge

Work out ∛125.

1Label the cube.
125?5?5?5
2Edge × edge × edge.
5×5×5
=25×5=125
3Write the answer.
∛125 =5

Work out ∛27.

1Label the cube.
27?3?3?3
2Edge × edge × edge.
3×3×3
=9×3=27
3Write the answer.
∛27 =3
1cubesedgeedgeedge2edge×edge×edge=layer×edge=cubes3∛cubes=edge

Work out ∛64.

1Label the cube.
64?4?4?4
2Edge × edge × edge.
4×4×4
=16×4=64
3Write the answer.
∛64 =4

1cubesedgeedgeedge2edge×edge×edge=layer×edge=cubes3∛cubes=edge

1Work out ∛1.

1
1?1?1?1
2
1×1×1
=1×1=1
3
∛1 =1

2A big cube is made from 27 small cubes. How many small cubes are along each edge?

1
27?3?3?3
2
3×3×3
=9×3=27
3
Along each edge =3

3Work out ∛1000.

1
1000?10?10?10
2
10×10×10
=100×10=1000
3
∛1000 =10

Is it right?
Thumbs up: right. Thumbs down: wrong.

  1. 23 = 6

    Wrong: 2 × 2 × 2 = 8

  2. ∛27 = 3

    Right: 3 × 3 × 3 = 27

  3. 103 = 1000

    Right

  4. ∛8 = 4

    Wrong: 2 × 2 × 2 = 8

  5. 43 = 64

    Right

Cubes and cube roots worksheet, page 1

Cubes and cube roots worksheet, page 2

Answer sheet

  1. A big cube has 6 small cubes along each edge. How many small cubes make the big cube?

    216

  2. Find a number between 1 and 100 that is a square number and a cube number.

    64

  3. ∛30 is between two whole numbers. Which two?

    3 and 4

  1. Work out 33.

    27
    1Label thecube.3332Edge × edge× edge.××=×=3Write theanswer.33 =

  2. Work out ∛64.

    4
    1Label thecube.???2Edge × edge× edge.××=×=643Write theanswer.∛64 =

  3. Work out 53.

    125
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