## Sunday, 24 February 2013

### MULTINOMIAL EXPANSION TUTORIAL

Hello readers, we have recorded our first tutorial video and you can check it out on YouTube :

We hope you guys like it. Feel free to leave your valuable remarks and suggestion in the comment box below.

PS- To check out more tutorials (non Math), check out our friend's blog : LINK

KEEP ON MATHEMATING!!

## Wednesday, 13 February 2013

### DIGITAL ROOT- ADD EM' UP!!

The concept of digital root is one of the most neat and easy concept in Mathematics. It helps explain many problems and further exemplifies the beauty of Math.

Digital Root of any number is the smallest single digit number that one obtains upon adding all the numbers present in a number. The digital root of 39, for instance is 3+9=12=1+2=3.

Digital Root showcases the beauty of Mathematics because the numbers of all the major sequences and series, like squares, cubes, Fibonacci series et al show a repetitive pattern in their digital root:

SQUARES
 SQUARE DIGITAL ROOT 1 1 4 4 9 9 16 7 25 7 36 9 49 4 64 1 81 9 100 1 121 4 144 9 169 7

If one observes closely, the digital root starts showing a repetition after 9, i.e. a set of 9 consecutive square numbers shows this repetitive pattern. So, the next set showing this pattern will be from 10-18, then 19-28 and so on...

CUBES
 CUBE DIGITAL ROOT 1 1 8 8 27 9 64 1 125 8 216 9 343 1 512 8 729 9 1000 1 1331 8 1728 9
Cubes follow an even shorter pattern; a set of only 3 consecutive cubes i.e. 1-3, 4-6 and so on...

INTERESTING FACTS
·
•     If you are careful enough, you might have seen that if 9 is added to any number ‘n’, the digital root of the sum will be equal to digit root of ‘n’. In simpler words, the addition of 9 to a number doesn't produce a change in the digital root.

•     The above fact helps us locate a multiple of 9. So if someone asks you for a multiple of 9 closest to the number 37218, simply obtain the digital root of 37218 (3) and then you have two options, you can either add 6 to get 9, or subtract 3 from the number; but because we are concerned with the closest number, we must subtract 3, which gives us 37215 whose digital root is 9, hence proving that it is a multiple of 9. This particular method is very useful in larger numbers

·       FUN FACT-
After lots of adding up and messy calculations, we both found out that 14 or FOURTEEN is the first number whose digital root is equal to the digital root of the numerical values of the alphabets of its spellings!!! They both equal 5!

We encourage our readers to perform their own operations and share any observations with the Mathematics world via our blog!!