Advanced International Journal for Research

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Volume 6 Issue 6
November-December 2025

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Practical formula for finding the square of two-digit numbers mentally

Author(s) Mr. Eray Aram Ilter, Sonay Ozturk
Country Turkey
Abstract Our primary goal in this project was to instill a love of mathematics in middle school students and unlock its secrets. We reasoned that middle school students spend a long time calculating the squares of two-digit numbers and sometimes make simple mistakes. Students often make simple mistakes even when solving these problems with pencil and paper. In this process, we wanted to calculate the square of a two-digit number mentally, using a practical, fast, and accurate formula. We found examples and calculated the squares of two-digit numbers. We tried to find the simplest formula. While working on the examples, we realized there was an algorithm for finding the solution and formalized it. We discovered that formulas had already been developed. However, the new formula we developed had to be much simpler and more memorable than the old ones, avoiding complex calculations. Therefore, we used the nearest tenth to the number we were squaring, discovered a relatively simple algorithm, and developed a new formula. Our experiments revealed that previously used formulas were more complex, but ours was more practical, easy to calculate, avoided complex operations, and was more memorable. With our formula, we used simple operations to calculate the square of a two-digit number by rounding to the nearest ten. This made it possible to perform the square calculations mentally. This formula, which allows us to calculate the square of two-digit numbers without using paper and pencil, allowed us to perform these complex calculations using simple multiplication, addition, or subtraction of simple numbers.
Keywords Two-digit number, square,
Field Mathematics > Logic
Published In Volume 6, Issue 6, November-December 2025
Published On 2025-11-11
DOI https://doi.org/10.63363/aijfr.2025.v06i06.1626
Short DOI https://doi.org/g998rr
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