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.

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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🏁 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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