Speed calculation · lesson 25 of 25 · free

Squares near 50 — Speed Calculation

50² is 2500, and every square from 41² to 59² follows one neat pattern. Find how far the number is from 50 — the gap. Add the gap to 25 (or take it away below 50) for the first part, then write the gap squared as two digits.

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The fast method

From 25 and the gap — “first part 25 ± gap, last two digits gap²”

  1. Find the gap from 50: 53 is 50 + 3, 46 is 50 − 4.
  2. First part: 25 + gap above 50, or 25 − gap below 50.
  3. Last two digits: the gap squared, written as 2 digits — 3² = 09.
  4. Join them: 53² = 28|09 = 2809.

Use it for: Areas of squares, Pythagoras and algebra in Class 8–10, and olympiad mental rounds.

Worked example: 46² = 2116

  1. 46 is 50 − 4.
  2. 25 − 4 = 21.
  3. 4² = 16, so 21|16 = 2116.

Check: 46 × 46 = 46 × 40 + 46 × 6 = 1840 + 276 = 2116 ✓

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✓ Written and checked by the TalentJR team · Updated 13 Oct 2026 · How we make our lessons

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🏁 Lesson 25 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass — and beat the clock: finish within 3 min.

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🖨️ Squares Near 50 Worksheet

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