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Lesson · Grade 8 · Mathematics

Perfect squares and perfect cubes: building them from tiles and cubes

  • Grade 8
  • Mathematics
  • 2 min 23 s
  • British Columbia
  • BC8-MA-01

36 tiles make a 6 by 6 square, so 36 = 6², which is 6 × 6 and not the common mistake 6 × 2 = 12. 30 tiles fall between 5 × 5 and 6 × 6 and make no square, while 27 small cubes stack into a 3 by 3 by 3 cube, so 27 = 3³. The video then lists the squares of 1 to 12 and the cubes of 1 to 5 and ends on a one-line recap.

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In one sentence

The question this lesson answers

Can 36 square tiles make one big square?

Yes: 6 rows of 6 tiles. Each side is 6 tiles long, and 6 times 6 is 36.

Transcript

What the lesson says

Can 36 square tiles make one big square?

Yes: 6 rows of 6 tiles. Each side is 6 tiles long, and 6 times 6 is 36.

So 36 is a perfect square: a whole number times itself.

We write 6 with a small raised 2, and say 6 squared.

The small 2 is the exponent. It tells us how many 6s are multiplied.

A common mistake is to read 6 squared as 6 times 2. That is only 12.

6 squared means 6 times 6, which is 36.

Take away 6 tiles to leave 30. Can 30 tiles make a square?

A 5 by 5 square uses 25 tiles, with 5 left over.

A 6 by 6 square needs 36. Even with the 5 spare tiles, we are 6 short.

30 is between 5 squared, 25, and 6 squared, 36, so it is not a perfect square.

Now stack 27 small cubes in 3 by 3 layers: 9, 18, 27.

The big cube is 3 long, 3 wide and 3 high, and 3 times 3 times 3 is 27.

So 27 is a perfect cube: a whole number used as a factor 3 times.

We write 3 with a small raised 3, and say 3 cubed.

Here are the squares of 1 up to 12: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.

And the cubes of 1 up to 5: 1, 8, 27, 64, 125.

So 6 squared, 6 times 6, is the perfect square 36, and 3 cubed, 3 times 3 times 3, is the perfect cube 27.

Curriculum

Where this fits

British Columbia, Grade 8

Mathematics, Number: perfect squares and cubesBC8-MA-01

Next: Spotting Perfect Squares and Cubes from Prime Factors

The outcomes and strands follow the British Columbia curriculum.

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