Mental maths · lesson 23 of 28 · free

Square any 2-digit number: up and down — Mental Maths Mastery

To square a number, move it up to the nearest round number and move it down by the same amount. Multiplying those two is easy because one of them ends in 0 — then just add the square of how far you moved.

How to do it in your head

Up and down — “go the same distance up and down to a round number, multiply, then add the distance squared”

  1. Find how far the number is from the nearest ten (the distance).
  2. Go that distance up and the same distance down, and multiply the two new numbers.
  3. Add the distance squared.

Use it for: Squares for Class 7–9, area of a square, and quick checks of square roots.

Worked example: 73² = 5329

  1. 73 is 3 away from 70: go down to 70 and up to 76.
  2. 70 × 76 = 5320 (7 × 76 = 532, then a 0).
  3. 3² = 9, and 5320 + 9 = 5329.

Check: 73 × 73 = 73 × 70 + 73 × 3 = 5110 + 219 = 5329 ✓

✏️ Practice

Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.

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🏁 Lesson 23 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

🏅 Sign in with Google to earn the 🎢 Up-Down Squarer badge when you pass — and a certificate when you finish all 9 lessons of Part 4 · Bigger numbers, fractions and the calendar. You can still take the test without signing in.

🖨️ Squaring 2-Digit Numbers Mentally Worksheet

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