Poonia4India : Shortcut to find cube of any number from 1 to 100

Finding cube of a number above 20 in the usual way is difficult and time consuming.
With this math trick you can easily calculate cube of a number within seconds.

Here is that trick


Step 1: Assume the ten's place number of the given number as a and the unit's place number as b.
Step 2: Now, we all know that (a+b)³=a³ + 3a²b + 3ab² + b<sup>3

We shall manipulate the same formula to calculate the cube of a number.</sup>

(i)Find b³ to get the last digit  

 If you get two digit number then, add ten's place digit to 3ab²

(ii) Find 3ab²  

     If you get two digit number then, keep the unit's place digit and and 
add ten's place digit to 3a²b.

(iii) Find 3a²b
      If you get two digit number then, keep the unit's place digit and and 
add ten's place digit to a^3.

(iv) Find a³

       If you get two digit number then, just add the carried forward digit if any
 and write the number.

    Cube of any 2 digit number will be in the pattern of
     a³ 3a²b  3ab² b³

    Cube To make things easier it is good to memorize the cubes of numbers from 1 to 10
     1³=1
     2³=8
     3³=27
     4³=64
     5³=125
     6³=216
     7³=343
     8³=512
     9³=729

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Lets use this method to calculate the cube of a number with help of an example to understand better

Example 1: (32)³=?
Step 1: Assume a= 3 and b= 2
Step 2: Now substituting the values of a and b in the below pattern
              a³ 3a²b  3ab² b³           

(i) Finding b³  Now that is 
     b³=2³=8
   We get the last digit as 8.

(ii) Finding 3ab^{2
    3ab2=3(3)(2)2=36
    From this we will keep the one's place digit(6) and add the ten's place digit(3) to 3ab.}

 (iii)Finding 3ab and adding ten's place digit(3)
     <sup>3a2b=3(3)2(2)=3(9)(2)=54 + 3= 57
     From this we will keep the one's place digit(7) and add ten's place digit(5) to b in the next        step. 

 (iv)</sup> Finding a³ and adding the ten's place digit(5) from previous step
     <sup>a3=33=27+5=32
     From this we get the number as 32  

  From all the above steps we get</sup> 

     (32)³=32768




Example 2:(47)³=?
Step 1: Assume a= 4 and b= 7
Step 2: Now substituting the values of a and b in the below pattern
              a³ 3a²b  3ab² b³           

(i) Finding b³  Now that is 
     b³=7³=343
   We get the last digit as 3.

(ii) Finding 3ab^{2  
    3ab2=3(4)(7)2=12 x 49=588 (Tip: Use Shortcut to multiply any 2 digit by 2 digit)
    Now add 34 that you got from step 1 to 588,we get  588+34=622
    From this we will keep the one's place digit(2) and add remaining digits(62) to 3ab2.}
    

 (iii)Finding 3a²b and adding remaining digits of step 2(62)
     <sup>3a2b=3(4)2(7)=16 x 21=336 
     336+ 62=398
     From this we will keep the one's place digit(8) and add remaining digits(39) to a3.

 (iv)</sup> Finding a³ and adding the remaining digits from step 3
     ^a3=43=64
     64 + 39=103
     
    From all the above steps we get 
    47³=103823