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

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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 + b3

We shall manipulate the same formula to calculate the cube of a number.

(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 a3.

(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



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 3ab2
    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)

     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) Finding a3 and adding the ten's place digit(5) from previous step

     a3=33=27+5=32
     From this we get the number as 32  

  From all the above steps we get 


     (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 3ab2  
    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)

     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) 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
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