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    You are at:Home»Math Tricks»Shortcut Methods for finding the Cube of a number | number cube tricks
    Math Tricks

    Shortcut Methods for finding the Cube of a number | number cube tricks

    sivaalluriBy sivaalluriNovember 10, 2017Updated:January 4, 2025No Comments5 Mins Read

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    •   Easy methods for Cube of a Number | cube of a number calculator
      • Method : 1 (Cube of a Number End with Zero )
      • Method: 2 ( Cube of a number just near ten places)
      • Method : 3 (Cube of two-digit number).
      • Method : 4 ( Cube of any number).

      Easy methods for Cube of a Number | cube of a number calculator

    A cube of a number means that if any number is multiplied by itself three times, then the product is called the cube of that number.

    Generally, the cube of a number denoted as 3 is written a little up to the right of the numbers.

    Here Discussed different easy methods to find the cube of a number without a calculator. It will help all students to do fast calculations in their regular and commutative exams.

    First, remember the cube of a number from 1 to 10. 

    ( 1³= 1 ;

    2³= 8 ;

    3³= 27 ;

    4³= 64 ;

    5³= 125 ;

    6³= 216 ;

    7³= 343 ;

    8³= 512 ;

    9³= 729 ;

    10³= 1000 )

    As per the given number we can choose the method for the cube of that number

    Method : 1 (Cube of a Number End with Zero )

    Ex. 1 : Find the cube of  70 ( 70³= ? )

    Simply we can write the value of  7³  and add three zeros in the right side. i.e 7³  = 343  and  70³ = 343000

    Method: 2 ( Cube of a number just near ten places)

    Ex. 1 : Find the cube of 11 ( 11³= ? )

    Use the simple algebra formula  (a + b)³ = a³ + 3a²b + 3ab² + b³. 

    we can write 11³  = ( 10 + 1 )³ . So here take a = 10 , b = 1 then

    ( 10 + 1 )³ = 1000 + 300 + 30 + 1 = 1331.

    Ex. 2 : Find the cube of 48 ( 48³= ? )

    Use the simple algebra formula  (a – b)³ = a³ – 3a²b + 3ab² – b³. 

    we can write 48³  = (50- 2 )³ . So here take a = 50 , b = 2 then

    ( 50 – 2 )³ = 125000 – 15000 + 600 – 8 = 110592.

    Method : 3 (Cube of two-digit number).

    Ex. 1 : Find the cube of  68 ( 68³= ? )

    Take formula (a + b)³ = a³ + 3a²b + 3ab² + b³.  and here assume  Here, a = 6 and b =8.

    Step 1 : Take b³ = 8 x 8 x 8 = 512. Take the lost digit into the answer’s last place and the remaining value to be added to the next step.

    i.e Ans:  _ _ _ _ _ 2  and 51 are to be added in the next step.

    Step 2: Take 3ab² = 3  x 6 x 64 =  3 x 384 = 1152 and 51 ( from the previous step). So 1152 + 51 = 1203. Here Take the lost digit into the answer next place and the remaining value to be added to the next step.

    i.e Ans :  _ _ _ _ 3 2  and 120 are to be added in the next step.

    Step 3 : Take 3a²b =(3  x 36 x 8) + 120=  864 + 120 = 984.  Here Take the lost digit into the answer next place and the remaining value to be added to the next step.

    i.e Ans :  _ _ _43 2  and  98 are to be added in the next step.

    Step 4 : Take a² =(6 x 6 x 6) + 98=  216 + 98 = 314.  Take this value into the answer next place.

    i.e  Ans : 31443 2.

    Therefore, (68)³ = 314432.

     Easy methods for Cube of a Number | cube of a number calculator

    Method : 4 ( Cube of any number).

    Ex. 1 : Find the cube of  728 ( 728³= ? )

    Step 1: Split the number as like i.e  7 – 28 or 72 – 8.

    Here we take 72 – 8.

    Step 2 : Divide the 1st part by the 2nd part. i.e 72/8 = 9. Here we can take a = 8 , b= 9 , c = 8³ = 512

    Step 3 : Cube of 1st part c = 8 x 8  x 8 = 512. Here Take the last digit in the answer and the remaining value 51 to be added to the next step.

    i.e Ans:  _ _ _ _ 2  and 51 are to be added in the next step.

    Step 4 : 3 bc + 51= (3 x 9 x 512) +51=  13824 + 51 = 13875 . Here Take the lost digit into the next digit in the answer and the remaining value 1387 to be added to the next step.

    i.e Ans:  _ _ _ 5 2  and 1387 are to be added in the next step.

    Step 5 : 3 b² c +13875= (3 x 9 x 9 x 512) +1387= 124416 + 1387 = 125803 . Here Take the lost digit into the next digit in the answer and the remaining value 12580 to be added to the next step.

    i.e Ans:  _ _ _3 5 2  and  12580 are to be added in the next step.

    Step 6 : b³ c +12580= ( 9 x 9 x 9 x512) +12580= 373248 + 12580 = 385828. Here Take this value into the answer

    i.e Ans:  385828352.

    shortcut methods for finding the cube of a number | number cube tricks

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    Hi friends Thanks for reading. I hope you like it. Give feedback, comments and please don’t forget to share it

     

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