The Trachtenberg System provides a universal method for squaring any number. It's a direct application of the General Multiplication method, where you simply multiply a number by itself.
We build the answer from right to left. The rule for each digit of the answer simplifies because the "outer pair" and "inner pair" of digits are the same, leading to doubled products.
The final answer is 1,156.
Enter any number to see the step-by-step squaring process.
No, it's actually the exact same method! Squaring a number just means multiplying it by itself. The process is identical to the general 'pair-product' method, but some patterns emerge, like the middle term always being a doubled product (e.g., (a x b) + (b x a) = 2ab).
Yes! The Trachtenberg system also includes special, faster rules for squaring numbers that end in 5 or 6. The method taught here is the general one that works for any number.
The number of pairs you need to sum increases for the middle digits of the answer, so it does require more concentration. However, because the process is so consistent, it's often still easier and less error-prone than writing out long multiplication by hand.