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Lesson · Grade 8 · Mathematics

Cube roots: the edge of a cube from its volume

  • Grade 8
  • Mathematics
  • 2 min 12 s
  • British Columbia
  • BC8-MA-04

A cube with a volume of 125 cm³ has edges of 5 cm, because 5 × 5 × 5 = 125, so the cube root of 125 is 5; the same check gives ∛8 = 2 and ∛1000 = 10. The video also shows that dividing by 3 is a mistake, because 125 ÷ 3 ≈ 41.7 gives three numbers that add to 125, not three that multiply to make it.

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In one sentence

The question this lesson answers

The volume of this cube, the space it takes up, is 125 cubic centimetres. How long is each edge?

An edge is a line where two faces meet. All the edges of a cube are the same length.

Transcript

What the lesson says

The volume of this cube, the space it takes up, is 125 cubic centimetres. How long is each edge?

An edge is a line where two faces meet. All the edges of a cube are the same length.

To find the volume of a cube, multiply edge times edge times edge.

So which number, multiplied by itself three times, makes 125?

Try 4: 4 times 4 times 4 is 64, which is too small.

Try 5: 5 times 5 is 25, and 25 times 5 is 125. So each edge is 5 centimetres.

5 is called the cube root of 125: the number that, multiplied by itself three times, makes 125.

This is the cube root sign. Its small 3 means that three equal numbers are multiplied.

In the same way, a cube of 8 cubic centimetres has edges of 2 centimetres, because 2 times 2 times 2 is 8. So the cube root of 8 is 2.

A cube of 1000 cubic centimetres has edges of 10 centimetres, because 10 times 10 times 10 is 1000. So the cube root of 1000 is 10.

A common mistake is to divide by 3. But 125 divided by 3 is about 41.7.

Check it: 41.7 times itself three times is far more than 125, so it is not the cube root.

Dividing by 3 gives three equal numbers that add to 125. A cube root needs three equal numbers that multiply to 125.

So the edge of a cube is the cube root of its volume: the cube root of 125 is 5, because 5 times 5 times 5 is 125.

Curriculum

Where this fits

British Columbia, Grade 8

Mathematics, Number: square and cube rootsBC8-MA-04

Previous: Square roots: the side of a square from its areaNext: Estimating √30 Between Two Perfect Squares

The outcomes and strands follow the British Columbia curriculum.

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