SUBJECTNEST · YEAR 11 MATHEMATICAL METHODS · ORIGINAL OFFLINE AID

Find the square hiding inside

Enter a positive whole number. This explorer finds its largest perfect-square factor and shows an exact root alongside a decimal check. Work out your own factor first, then compare. It does not solve symbolic algebra or make a real-world measurement.

Exact value and check

Paper route

  1. List squares no larger than the number: 1, 4, 9, 16, 25, …
  2. Choose the largest square that divides the number exactly. Write n = square × remainder.
  3. Take the square root of the square factor out. If the remainder is 1, the result is a whole number.
  4. Square your exact result to check it gives the original number. Use a decimal only as an approximate sense check.

Example: 72 = 36 × 2, so √72 = 6√2 exactly. Squaring 6√2 gives 72. The decimal √72 ≈ 8.4853.

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