# Digital root

Digital root (Digit sum) of a number is a result of the progressive summation of the digits of a number, i.e. given a number N1, all the digits of N1 are added to obtain N2. All the digits of N2 then are added to obtain a number N3 and so on till a single digit number N is obtained. This single digit numberN is called the digit sum or the digital root of the original number N1. For example, In 9575621, 9 + 5 + 7 + 5 + 6 + 2 + 1 = 35 = 3 + 5 = 8 is the digit sum.

## Digit root rules

Multiplication

The digit sum of the product of two number is equal to the digit sum of the sum of the product of the digit sums of the two numbers. For example,

245 x 1932 = 473340

Digital roots of 245, 1932 and 473340 are 2, 6 and 3 respectively. 2 x 6 = 12 which has its digital root as 3.

Power of 9

If one of the multiplicands is 9, then the digital root will always be 9.

Perfect squares

Digital roots of all perfect squares can only be one amongst 1, 4, 9 or 7. It is a quick method to check if a number is not a perfect square. If a number has a digital root of 1, 4, 7 or 9 it may or may not be a perfect square.

### Relevant exercises

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