Finding square roots can be difficult but using the Trachtenberg System of finding square roots I find the method easy and interesting. The method comes at the answer from both sides, in fact you use the answer you get to confirm if you have indeed got the right answer and if there is any remainder.

Finding the size of the Square Root


Before starting any calculation you can accurately know the size of the square root, that is how many figures it will contain. The rule to find the size of the square root is:

  • If the number has an even number of figures then the square root will contain exactly half as many figures.
  • If the number has an odd number of figures then add one to the number of figures. The square root will contain half this number of figures.

We will look at a few examples.

657 has three figures, so 3 + 1 = 4 and half of four is two which is how many figures the square root will have.
4832 has four figures, half of four is two so this also has a two figure square root.
817345721 has nine figures, so 9 + 1 = 10 and half of ten is five. This number has a five figure square root.

The Trachtenberg system method for finding square roots can be used for three figure numbers up to ten figure numbers. The method for 3 or 4 figure numbers is quite simple and gets more involved as the number size increases. To be honest I can do the method for finding the square root of 9 or 10 digit numbers but I have to write it down as I cannot keep that many numbers in my head.