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 theten's place numberof the given number asaand theunit's placenumberasb.
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 b3to get the last digit
If you get two digit number then, add ten's place digit to 3ab2
(ii) Find3ab2
If you get two digit number then, keep the unit's place digit and and
add ten's place digit to3a2b.
(iii) Find3a2b
If you get two digit number then, keep the unit's place digit and and
add ten's place digit toa3.
(iv)Finda3
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
a 33a2b 3ab2b3
Cube To make things easier it is good to memorize the cubes of numbers from 1 to 10
1 3=1
2 3=8
3 3=27
4 3=64
5 3=125
6 3=216
7 3=343
8 3=512
9 3=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
a33a2b 3ab2b3
(i) Findingb3Now that is
b3=23=8
We get the last digit as 8.
(ii) Finding3ab2
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 a3and 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
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