Here we will have a look at what a digital root, or digit root, is and how you can make use of it.

We will not be going into the math behind why using digital root works, after all this is supposed to be a site on basic mathematics, but for those who are interested you can find out more in wikipedia about digital root.

Digit Sum and Digital Root


There is another term you may have heard which is the Digit Sum, or Digital Sum, which seems to have two meanings. The first being the sum of the digits of a non-negative integer (e.g. 0, 1, 2, ..., 9999, etc) and the second being the same as the Digit Root.

If we take the number 15785 we can calculate the digit sum as follows:

    \[    \text{The digit sum of } 15785 = 1 + 5 + 7 + 8 + 5 = 26 \]

To find the digit root we repeat the digit sum on the sum we just calculated and if necessary repeat again until the sum has only one digit.

    \[   \text{The digit sum of } 26 = 2 + 6 = 8 \]

So therefor the digit root of 15785 is 8.

Lets have a look at another example.

    \begin{equation*}   \begin{split}     23567 &= 2 + 3 + 5 + 6 + 7 = 23\\        23 &= 2 + 3 = 5    \end{split} \end{equation*}

For 23567 the digit sum is 31 and the digit root is 5.

Now we know what a digit root is what can we do with it?

Checking your results


When doing a calculation whether it is addition, subtraction, multiplication, division, squaring a number or finding a square root it would be nice to be able to check your results without having to repeat the whole equation again.

The problem with simply redoing a calculation to check it is that you may make the same mistake again and simply confirm the incorrect result. Using the digit root allows you to recheck the calculation to see if it is correct or not but because your using a different method you are not able to repeat any mistake.

The digit root as we have shown is also referred to as "casting out nines" but there is also another similar method known as "casting out elevens" which also uses a digit root but the root is found by a different method.

Neither of these methods were developed as part of the Trachtenberg Speed Math System but were integrated into it as ways to check and double check your results because it is not enough to simply arrive at an answer we should also confirm that we have the right answer. Before the hand held calculator the casting out nines method was a common way to recheck your calculations and dates back to the ancient Greeks.

We will show you both casting methods and how they can be used with the various types of equations mentioned above.