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Lesson · Grade 8 · Mathematics

Square roots: the side of a square from its area

  • Grade 8
  • Mathematics
  • 2 min 4 s
  • British Columbia
  • BC8-MA-03

A square with an area of 49 cm² gets 7 cm sides by finding the number that times itself makes 49, checked with a 7 by 7 grid, which introduces squaring and the square root (√49 = 7) as steps that undo each other for positive numbers. The same square then has an area of 16/169 cm², giving √(16/169) = 4/13 cm, checked by squaring; the video then corrects the common mistake of halving (√16 is 4, not 8, since 8 × 8 = 64) and ends on the recap √49 = 7, because 7 × 7 = 49.

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In one sentence

The question this lesson answers

A square has an area of 49 square centimetres. How long is each side?

The area of a square is its side length times itself.

Transcript

What the lesson says

A square has an area of 49 square centimetres. How long is each side?

The area of a square is its side length times itself.

Which number times itself makes 49? 6 times 6 is 36, too small. 7 times 7 is 49.

So each side is 7 centimetres: 7 rows of 7 small squares make 49.

Multiplying a number by itself is called squaring it. 7 squared, written with a small 2, is 49.

Going back the other way is called taking the square root. The square root of 49 is 7.

Here the square root sign asks for the positive number that, times itself, gives 49.

So for positive numbers, squaring and taking the square root undo each other.

Now a square with an area of 16 over 169 square centimetres. Its side is the square root of 16 over 169.

Take the square root of the top and of the bottom: 16 gives 4, and 169 gives 13.

So each side is 4 over 13 of a centimetre.

Check by squaring: 4 times 4 is 16, and 13 times 13 is 169.

A common mistake is halving: half of 16 is 8, but the square root of 16 is not 8.

8 times 8 is 64, not 16. 4 times 4 is 16, so the square root of 16 is 4.

Recap: a square's side is the square root of its area. The square root of 49 is 7, because 7 times 7 is 49.

Curriculum

Where this fits

British Columbia, Grade 8

Mathematics, Number: square and cube rootsBC8-MA-03

Previous: Spotting Perfect Squares and Cubes from Prime FactorsNext: Cube roots: the edge of a cube from its volume

The outcomes and strands follow the British Columbia curriculum.

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