NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Squares and square roots

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Required skills (click to reveal)

A square-shaped floor in Brisbane is tiled with 169 identical square tiles. Using the relationship between perfect square numbers and their square roots, what is the exact length of one side of the floor in terms of the number of tiles?

Express your answer as an exact number.

Concept illustrations

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A square with area forty-nine. 49 unit squares form a 7 by 7 square. √49 = 7.7 units across7
49 unit squares form a 7 by 7 square. √49 = 7.
Four squared. 4² = 4 × 4 = 16 unit squares.4 units across4
4² = 4 × 4 = 16 unit squares.

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The floor is square-shaped and tiled with 169 identical square tiles. The total number of tiles is 169, which represents the area of the floor in terms of tile units.
  2. Since the floor is square, its area equals the side length squared. Therefore, if the side length in tiles is s, then s² = 169.
  3. To find s, take the square root of 169. This uses the relationship between perfect square numbers and their square roots.
  4. 169 is a perfect square because it is 13 × 13. This can be verified by checking that 13² = 169.
  5. Therefore, sqrt(169) = 13. This means the side length of the floor is 13 tiles.
  6. The question asks for the length of one side in terms of the number of tiles. Since the tiles are square and arranged in a grid, the side length is exactly 13 tiles.
  7. No conversion is needed because the answer is required in tile counts, not physical length.
  8. Check: 13 × 13 = 169. This confirms that 13 is the correct square root of 169.
  9. The result is an integer, so no approximation is needed.
  10. The floor has 169 tiles, arranged in a square pattern, so the side must be 13 tiles long.
  11. The answer is exact and matches the requirement: the side length in number of tiles.
  12. Final answer: 13 tiles.

Reference answer: 13

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