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Vedic Mathematics - Easy and Faster Calculation of Cubes

Updated on November 1, 2009
Calculating Cubes faster
Calculating Cubes faster

Calculating Cubes easy and faster

To find out cubes of the two digit number, we generally take help of the following formula:

(a+b)’cubes= a’cube+3a’square b+ 3ab’square +b’cube.

This can be written as:

  a’cube +a’square b+ab’square +b’cube

  2a’square b 2 a b’square
  --------------------------------

  We have simply broken 3a’square b and 3ab’square in to two parts a’square and a b’square and 2 a b’square, to simplify the matter.
  In the above formula, we see that the terms a’cube, a’square b, a b’square and b’cube are placed at the top and the 2a’squareb and 2ab’square are placed at the bottom.
The complete formula comes into being when you add the terms at the top to those at the bottom.
If we scrutinize the top term closely, then we find that:
A’cube x b/a=a’square b
A’square b x b/a= a b’square and a b; square and a b’square x b/a= b’cube
The common ratio between the top terms is b/a. this is the ultimate finding. We have to dig out b/a and our desired result will be there. Let me explain with the help of the example:

1 2’cube, we have a=1,b=2 and b/a=2
a b

Steps:
• Our first term is a’cube= 1’ cube=1.
• The second term is a’square b= a’ cube x b/a= 1x2=2.
• The third term is a b’square= a’square b x b/a= 2x2=4.
• The fourth term is b’ cube= a b’square x b/a= 4 x 2=8.
• Put all this in the first row, maintaining a space.
• For the second row, double the two middle terms i.e. a’ square b=2 so that 2 a’ square b=4 and a b’square=4 so 2 a b’square=8.Second row comes as 4 and 8.
• Now add them

  1 2 4 8  
  4 8
  -----------------
  1 7 2 8- Answer
  1 - Remainder at each stage


Let us find 16’ cube; here a=1, b=6 and b/a=6. a’cube=1
16’cube=1 6 36 216
12 72
4 0 9 6 -answer
  ----------------------------
3 12 21 --- Remainder at each stage.

Steps:
• From the digit in the right 216, the unit digit 6 is retained as a part of the answer and the remainder 21 is added to the left
• After adding remainder 21 to (36+72) we get 129. 9 is retained as a answer and 12 is added to the left
• On adding the remainder 12 to the left we get 30. 0 is retained and 3 is added to the left.
• Adding the digits on the extreme left gives 4. The answer is 4096. Our procedure is over now.



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      Bhaiya 2 years ago

      Awesmmmmm

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      nirav shah 4 years ago

      very easy method. I like it.

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      Akansha 5 years ago

      Ha! I learnt this at school, but this was clearer- I was trying to do it this way:-

      (a'square*a)+(a square*3b)+(b square*a)+(b square*b)

      then we took the last digit of each and carried the rest over to the next ...

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      K.R.Mohanraj 5 years ago

      It's Really amasing....

    • profile image

      Jitesh 5 years ago

      It's a magic

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      Shwetank pandey 5 years ago

      Its a heart breaking for me to see this formula here..of finding squares and cubes, I made this formula at my own..I told many of my friends that I made it few days back,they are very excited at my approach I think Its is a unique approach by me but. I was totally unaware of vedic mathematics, I am trying to make another formulaes at higher level

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      rajesh khanna 5 years ago

      Wow......!!!!! What an excellent short cut. I liked it .

    • profile image

      penta 5 years ago

      Thanks a lot, 2 simple

    • profile image

      KT 6 years ago

      Do you run an online class by any chance?

    • profile image

      Mahendra 7 years ago

      Wowwwwwwwwww!!!!!!!!!!1

    • profile image

      Umair Zubair Shaikh 7 years ago

      This is Awesome !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

    • profile image

      Mahima Kaushik 7 years ago

      This is an awsome site wid d best tricks.........really helpfull

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      Obhund 7 years ago

      Hi Saurabh!

      Thanks a lots for this hub.

      I was getting crazy try to understand, Vedic method for cubes and just your video make all clear and simply.

      Thanks again.

      Obhund

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      shubi  8 years ago

      I want exact method of finding cube roots using vedic maths. I want the methods in points i.e, in steps. THANX