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A Square and A Cube

Going back to the side you started from

A square patch has 361 tiles. How long is its side? The sign √ finds a square's side from its tiles. √361 is the side of this patch.

8 × 8 = 64 — squaring the side.
Step 1 of 4
  1. 8 × 8 = 64 — squaring the side.
  2. Going back: √64 = 8.
  3. A common wrong guess: √16 is half of 16, so 8.
  4. Check: 8 × 8 = 64, not 16. So √16 = 4.

The side is 19 tiles, so √361 = 19. Check: 19 × 19 = 361.

Rule: A square root is the side of a square. Check it: multiply the side by itself.

  • √1 = 1, √9 = 3, √36 = 6
  • √100 = 10, √121 = 11, √225 = 15

(−9) × (−9) = 81 too. So 81 has two roots, 9 and −9. A side cannot be below 0. So here we use the positive one: √81 = 9.

Slide the side until the tiles match the area.

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This track

  1. 0 Start here
  2. 1 A number you can draw as a square
  3. 2 Each new layer is the next odd number
  4. 3 A test that can only say no
  5. 4 Going back to the side you started from
  6. 5 Pairing the primes finds the side
  7. 6 Checkpoint: squares, the staircase and roots
  8. 7 When no whole number fits
  9. 8 A cube number counts real cubes
  10. 9 What cubes end in, and what they add up to
  11. 10 Grouping the primes in threes
  12. 11 Which count is the job asking for
  13. 12 Checkpoint: in between, cubes and cube roots
  14. 13 The big picture
  15. 14 Track quiz

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