Find the gap. Use it twice.
Square numbers near 100 in your head
An original website mini lesson · Learning On My Own
The idea
Find how far the number is from 100. That gap gives you both parts of the answer: the first two digits and the last two digits.
Worked example
94²
- 94 is 6 below 100.
- Take the gap away once more: 94 − 6 = 88. These are the first digits.
- Square the gap: 6 × 6 = 36. These are the last two digits.
- Put them together: 8836.
Why it works: 94² = (100 − 6)² = 100 × (100 − 6 − 6) + 6² = 8800 + 36.
Two things to watch
The last part always takes two digits. For 97², the gap is 3, so 97 − 3 = 94 and 3 × 3 = 9. Write the 9 as 09: the answer is 9409, not 949.
Above 100, add instead. For 103², the gap is 3 above, so 103 + 3 = 106 and 3 × 3 = 09. The answer is 10609.
Your turn
Find 96² without a calculator.
See the answer and steps
96 is 4 below 100. 96 − 4 = 92, and 4 × 4 = 16. So 96² = 9216.
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