5 Interesting facts about Digital sum and Digital roots

Have you ever gone through the topic called digital sum and surprised?
Don't worry if you have not yet gone through because this post is exclusively for people like you.
Solutions for these questions gets cleared after reading this post.
  1. What is Digital sum?
  2. How does digital sum help to save time?
  3. What is a Digital root?
Digital sum and digital root
Digital sum: Digital sum can be defined as the sum of all the digits of a number.
Digital root: The Digital root of a number can be obtained by finding digital sum repeatedly until you get a single digit.

Let A, B be two numbers.
Digital root properties:
  1. Digital root(A*B) = Digital root( Digital root(A)*Digital root(B) )
  2. Digital root(A^2) = Digital root(Digital root(A)*Digita root(B))
  3. Digital root(A+B) = Digital root( Digital root(A)+Digital root(B) )
  4. Digital root(A-B) = Digital root( Digital root(A)-Digital root(B) )
  5. Digital root(10^x + A) = Digital root(A)
How are these properties going to help you in saving your time?
If you got a question to pick a square of a number from four options, this method works very well most of the times.

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Question 1: What is the value of 997^2
options: A) 994009   B) 996009 c)997009 D)992009
Solution:
Digital root(997)= 9+9+7=> 25 (2+5)=> 7
Digital root(997^2) should be Digital root(7*7)=49(4+9)=>13(1+3)=>4
find the digital root of all the options
Digital root(994009)=9+9+4+0+0+9=31  (3+1)=>4
Digital root(996009)=9+9+6+0+0+9=33 (3+3)=>6
Digital root(997009)=9+9+7+0+0+9=34 (3+4)=>7
Digital root(992009)=9+9+2+0+0+9=29 (2+9)=>11 (1+1)=>2
Comparing the digial roots, the only possible option would be 994009.

This technique works well for most of the problems and helps you save your time.
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