Level 1 · Quick Tricks
Squaring Numbers Ending in 5
Square any number ending in 5 in two seconds flat — no calculator, no paper.
The Rule
For any number ending in 5, call the part before the 5 "X". Multiply X by X + 1, then append 25. The last two digits are always 25.
Worked Example
35²
- X = 3 (the digit before the 5)
- X + 1 = 4
- 3 × 4 = 12
- Append 25: 1225
Another Example
85²
- X = 8
- X + 1 = 9
- 8 × 9 = 72
- Append 25: 7225
Why It Works
Any number ending in 5 can be written as (10X + 5). Squaring it:
(10X + 5)² = 100X² + 100X + 25 = 100·X(X+1) + 25
The 100 shifts X(X+1) two decimal places left — which is exactly "X(X+1) followed by 25."
💡 Extension Challenge
This trick works for any number of digits ending in 5 — not just two-digit numbers. Try 125² in the sandbox.