Squaring numbers (multiplying a number by itself) is a special case of multiplication. The Trachtenberg system provides a streamlined way to do this, similar to the general multiplication method but optimized for squares.
For a two-digit number, it's very similar to the algebraic expansion . We work from right to left.
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.
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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.