How to Square a Number Ending in 5 in Your Head

Updated 12 October 2026

Instantly square numbers ending in 5

65 × 65 = 4225

How do you square a number ending in 5?

To square a number ending in 5, multiply its tens digit by the next whole number up, then write 25 after the result. For 65², the tens digit is 6 and the next number is 7, so 6 × 7 = 42 and 65² = 4225. The same step gives 35² = 1225, because 3 × 4 = 12, and 95² = 9025, because 9 × 10 = 90. It works because a number ending in 5 is 10n + 5, and its square is 100 × n(n + 1) + 25: the product lands in the hundreds and the 25 fills the last two places, so the two parts never overlap. For a longer number, treat everything before the 5 as one number: 145² starts with 14 × 15 = 210, so 145² = 21025. Check any answer by its ending, because the square of a number ending in 5 always ends in 25.

1. 65 × 65 is a square split at the tens: 3600, 300, 300 and 25.

2. The 3600 and both 300s make 60 × 70 = 4200. Only the 25 is left.

3. So the recipe: tens digit × one more, then attach 25. $65^2=4225$65² = 4225.

Does it work for three-digit numbers ending in 5?

Yes, and the part before the 5 can be any size. For $115^2$115², the number before the 5 is 11, so 11 × 12 = 132, then attach 25: 13225. For $205^2$205², 20 × 21 = 420, then attach 25: 42025.

Why does it work?

A number ending in 5 is 10n + 5. Squaring gives $100n^2+100n+25$100n² + 100n + 25, which is 100 × n × (n + 1) + 25. The n × (n + 1) is the tens digit times the next number, the × 100 puts two empty places after it, and the 25 fills those two places.

All 36 shortcuts: the Magic Tricks library.