Give me any 2 digit number that ends in 5, and I’ll square it in my head!

45^{2} = 2025

85^{2} = 7225, etc.

There’s a quick way to do this: if the first digit is N and the second digit is 5, then the last 2 digits of the answer will be 25, and the preceding digits will be N*(N+1).

**Presentation Suggestions:**

After telling the trick, have students see how fast they can square such numbers in their head, but doing several examples.

**The Math Behind the Fact:**

You may wish to assign the proof as a fun homework exercise: multiply (10N+5)(10N+5) and interpret! The trick works for larger numbers, too, although it may be harder to do this in your head. For instance 205^{2} = 42025, since 20*21=420. Also, you can combine this trick with other lightning arithmetic tricks. So 115^{2} = 13225, because 11*12 = 132, using the Multiplication by 11 trick.

The reference also contains more secrets of fast mental calculations.

**How to Cite this Page:**

Su, Francis E., et al. “Squares Ending in 5.” *Math Fun Facts*. <https://www.math.hmc.edu/funfacts>.

**References:**

A. Benjamin and M. Shermer, Secrets of Mental Math, Three Rivers Press, 2006.

**Fun Fact suggested by: **

Francis Su