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.

quickermaths

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.

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Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

110 thoughts to “Shortcut to find the Cube of a number”

    1. Ratio is 2:3
      Cube of Tens Digit is 8, i.e. cube of 2
      Now other four digits in geometric progression exactly as the ratio of question digits are
      8:12:18:27
      Now, twice of 2nd and 3rd number just below the respective numbers
      8:12:18:27
      + :24:36:
      8:36:54:27
      Now, let the no. 7 in own place and Carry over 2 to left it will become 56
      Now, let the no. 6 in own place and carry over 5 to the left it will become 41
      Now, let the no. 1 in own place and carry over 4 to the left it will become 12

      We get the answer as:
      12167

      1. I tried cube of 49 by this method it is coming out to be something different. Try it

    1. That’s the beauty of calculations. You can always do it your way. One should explore various ways doing calculations but adopt the one where he is most comfortable.

      Thanks

    1. Ratio is 8:8
      Cube of Tens Digit is 512, i.e. cube of 8
      Now other four digits in geometric progression exactly as the ratio of question digits are
      512:512:512:512
      Now, twice of 2nd and 3rd number just below the respective numbers
      512: 512 : 512 :512
      + : 1024: 1024:
      512:1536 :1536 :512
      Now, let the no. 2 in own place and Carry over 51 to left it will become 1587
      Now, let the no. 7 in own place and carry over 158 to the left it will become 1694
      Now, let the no. 4 in own place and carry over 169 to the left it will become 681

      We get the answer as:
      681472

  1. 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.

    1. 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.

    2. 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

    3. 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

  2. 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

    1. (57) KA CUBE = 5*5*5 5*5*7 5*7*7 7*7*7
      125 175 245 343
      350 490
      _______________________________________
      Now Simply Carry forward & add from R to L =185193
      _______________________________________
      This is how U can Solve d Cube Of any two digit Number .

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

    What is the quick, MENTAL, method ?

  4. 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 ??

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