Mental Math · Multiplication · M5
Two beautiful patterns. Any number ending in 5 squares instantly: multiply the tens digit by the next number, then write 25. And two numbers the same distance from a round number multiply with the difference-of-squares trick: 12 × 8 = 10² − 2².
Watch the method
For 35²: take the tens digit 3, multiply by the next number 4 to get 12, then write 25 on the end → 1225. It always works.
Take the tens digit 3 and multiply by the next number, 4.
Write 25 on the end — always.
Your turn
Use the method, then check. Stuck? Reveal the steps.
n5 squared = n(n+1) followed by 25. And a × b where both are d away from a round number m equals m² − d². 12 × 8: both are 2 from 10, so 100 − 4 = 96.
Why it works
Close pairs hug a round number — the product is the square of the centre minus the square of the gap.
25²
Front
2 × 3 = 6.
End
Write 25 → 625.
35²
Front
3 × 4 = 12.
End
Write 25 → 1225.
12 × 8
Centre
Both are 2 away from 10.
Difference of squares
10² − 2² = 100 − 4 = 96.
Writing the wrong ending for squares of 5s.
The last two digits are ALWAYS 25. Only the front part, n(n+1), changes.
Using difference of squares when the pair isn't symmetric.
Both numbers must be the same distance from the centre. 12 × 8 works (both 2 from 10); 12 × 9 does not.
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t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).15² = ?
25² = ?
35² = ?
45² = ?
55² = ?
65² = ?
75² = ?
85² = ?
12 × 8 = ?
13 × 7 = ?
21 × 19 = ?
95² = ?