Home » Speedy Calculation » Shortcut to find the Cube of a number

Very often we have to find the cube, i.e. third power of 2 digit numbers. Cubes of very large numbers are rarely used.

Cubes of all the single digits should be memorized. Find below the table of cubes of first ten natural numbers -

13 = 1,              23 = 8,              33 = 27,            43 = 64,            53 = 125,

63 = 216,          73 = 343,          83 = 512,          93 = 729,          103 = 1000

To find the cube of any 2 digit number, we have to take the following steps

First Step: The first thing we have to do is to put down the cube of the tens-digit in a row of 4 figures. The other three numbers in the row of answer should be written in a geometrical ratio in the exact proportion which is there between the digits of the given number.

Second Step: The second step is to put down, under the second and third numbers, just two times of second and third number. Then add up the two rows.

Finding the cube of 12

Or, 123 = ?

First Step: Digit in ten’s place is 1, so we write the cube of 1. And also as the ratio between 1 and 2 is 1:2, the next digits will be double the previous one. So, the first row is

1 2 4 8

Step II: In the above row our 2nd and 3rd digits (from right) are 4 and 2 respectively. So, we write down 8 and 4 below 4 and 2 respectively. Then add up the two rows.

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Ex 2: 163 = ?

Soln:

quickermaths

Explanations: 13 (from 16) = 1. So, 1 is our first digit in the first row. Digits of 16 are in the ratio 1:6, hence our other digits should be 1×6 = 6, 6×6 = 36, 36×6 = 216. In the second row, double the 2nd and 3rd number is written. In the third row, we have to write down only one digit below each column (except under the last column which may have more than one digit). So, after putting down the unit-digit, we carry over the rest to add up with the left-hand column. Here,

i) Write down 6 of 216 and carry over 21.

ii) 36 + 72 + 21 (carried) = 129, write down 9 and carry over 12.

iii) 6 + 12 + 12 (carried) = 30, write down 0 and carry over 3.

iv) 1 + 3 (carried) = 4, write down 4.

About

Hi, I'm Vineet Patawari. I fall in love with numbers after being scared from them for quite some time. Now, I'm here to make you feel safe with numbers and help you come out of Maths Phobia!

comments

  1. Manjesh Lodhi says:

    Its a good trick to find cube in less time

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  3. […] a shortcut to find the fourth power of any 2 digit number. The approach will be similar to the shortcut to find the cube of any 2 digit number. I strongly suggest that you should check that […]

  4. sabina says:

    cube of three digit number????

  5. haribansh says:

    i think it will be better to find the square and then multiply it using shortcut method.

  6. Mani says:

    Plese tell the method to find::

    The least number to be added with 1720 to make it as a perfect cube??

  7. TO FIND THE SQUARE OF A NO. WHOSE UNIT PLACE IS 5
    EG:-if wehave 2 find the square of 15 then multiply first 5*5 then multiply 1 with
    more than 1 i.e 1*2=2 & wite 2 before 25 i.e 225

  8. Hannah Aguaras says:

    THANK YOU SO MUCH!!!!!!!!

  9. Asif says:

    what is the method to find cube of 88,222,6666,…. etc. ?

  10. Asif says:

    what is the method to find cube of 222, 88, 6666…etc?

  11. mani says:

    how to find out cube of any number Ex:25,56,86 etc based on your find a cube of any number? i tried your method but i am not getting write answer.

    please guide me.

    • noops says:

      how to find out cube of any number Ex:25,56,86 etc based on your find a cube of any number? i tried your method but i am not getting write answer.
      please guide me.

    • Sumit Kumar says:

      It means that you are making mistakes in calculating. Here is the solution for
      25.
      Cube of 2, the first letter in the number is 8. Now put the next 3 numbers using the 2:5, that is,
      8 20 50 125
      40 100
      __________ Now start from the left.
      8 60 150 125
      8+60+(150+12)\5 = 8+60+162\5 = 8+(60+16)\25
      8+76\25
      (8+7)/625
      15625

    • Jugal says:

      STEP 1. TAKE ANY NUMBER U WANT TO FIND THE CUBE.

      STEP 2. WRITE THE CUBE OF THE DIGIT PLACE NUMBER..

      for eg: if 56 is the number… write the cube of 6.. ie 216

      STEP 3. WHATEVER ANS U GET WRITE ITS LAST DIGIT N CARRY THE REMNG NUMBERS..

      for eg: in above eg write 6 and carry 21

      STEP 4. THEN MULTIPLY BOTH THE DIGITS OF THE NUMBER U SELECTED TO FIND THE CUBE.AND AGAIN MULTIPLY THAT ANS BY 3.

      for eg: if u select 56… then multiply 5 and 6 ie 30 and multiply 30 by 3.. ie 90

      STEP 5: MULTIPLY THE ANS U GOT BY THE NUMBER U SELECTED TO FIND THE CUBE…

      for eg: ie in above eg multiply 90 by 56 ie = 5040

      STEP 6. NOW, CONSIDER ONLY THE LAST TWO DIGITS AND CARRY THE REMAINING OF THE ANS U GOT AND ADD THE LAST TWO DIGITS BY CARRY NUMBER IN STEP 3

      for eg: the carry number was 21 and the last two digit of ans is 40.. so add 40 and 21 ie=61

      STEP 7. NOW WRITE THAT NO. ON THE LEFT OF ANS U GOT IN STEP 2.

      for eg… cube of 6 216… u wrote 6 and carried 21.. by following step 5 and 6.. u got 41,,, so write it as … 416

      STEP 8: NOW FIND THE CUBE OF REMAINING DIGITS OF THE NUMBER U SELECTED AND ADD IT BY THE CARRY IN STEP 6.. AND WRITE THE ANS BESIDE STEP 7

      for eg: cube of number 5 in 56 is 125… add it by 50 (carry in step 6).. ie 125+50=175.. now write 175 beside 416… ie 175416

      STEP 9: THE CUBE OF UR NUMBER IS READY :)

      TRY IT IT IS MY INVENTION

      JUGAL

  12. jeevan says:

    short trick 1-30 cube

  13. SanthoshKumar Potnuru says:

    For eg:57
    5^3=125, 7^3=343
    5/7(343)=245
    5/7(245)=175 350=175*2,,,,,490=245*2
    125 175 245 343
    350 490
    ____________________
    185193

  14. ABHI says:

    one of the best websites for the pupil who attends competitive exams

  15. Kavita Anuragi says:

    How to calculate cube of 57, 83???

  16. ahmed says:

    This is a written method of calculating cubes of numbers by paper & pencil.

    What is the quick, MENTAL, method ?

  17. simple says:

    Nice way to calculate Cube ..how can we calculate cube of 23.

  18. simple says:

    Ho w to calculate cube of 23 ??

  19. ahmed says:

    This ” Vedic” method is OK if one has to *calculate* the cubes of numbers in writing.

    Do you have a method of getting these answers, totally by mental calculation, from inside ones head ??

  20. shubham says:

    very nice and quicker way to do mathematics

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Who is behind QuickerMaths?

I am Vineet Patawari - PGDM (IIM Indore), ACA, B.Com(H). My passion for Mathematics, specially Vedic Maths encouraged me to start QuickerMaths

I believe that if trained properly using powerful tools like Vedic Maths, the immense intellect of human mind can be ignited instantly - find out more

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