How to Cube a Number easily and quickly

The cube of a number is that number multiplied by itself twice. For example, 5 cubed - denoted as 53; is equal to 5×5×5 = 125. The technique for cubing any 2-digit number discussed below is based on the algebraic observation.
Step-1:       Write numbers in a row of 4 terms in such a way that the first one is the cube of the 1st digit, second one is the square of 1st number multiplied by 2nd digit, third one is the 1st digit multiplied by square of 2nd digit and the fourth one is the cube of the 2nd digit.
Step-2:      Write twice the values of 2nd and 3rd terms under the terms respectively in second row.
Step-3:      Add all the values column-wise and follow the carry over process.
Example: Find Cube of 14.

Step-1                             :        13       12×4   1×42   43
Worked-out row               :        1        4        16      64
Step-2                             :                  8        32     
Step-3                             :        Add the values column wise.       

First Column from Right: Bring down 4 and carry over 6.
         
1
4
8
16
32
64


6




4

Second Column from Right: 16+32+6=54. Bring down 4 and carry over 5.               
                  
1
4
8
16
32
64

5
6



4
4

Third Column from Right: 4+8+5 = 17. Bring down 7 and carry over 1.            
                  
1
4
8
16
32
64
1
5
6


7
4
4

Fourth Column from Right: 1 + 1 = 2. Write down 2.
How-to-cube-a-number-easily
1
4
8
16
32
64
1
5
6

2
7
4
4

This 2,744 is the cube of the number 14.

Another Example: Cube of 25 =?
         
Step-1

23
22×5
2×52
53
Worked-out

8
20
50
125
Step-2


40
100

Step-3
Carries




Sum





First Column from Right: Bring down 5 and carry over 12.
         
8
20
40
50
100
125


12




5

Second Column from Right: 50 + 100 + 12 = 162. Bring down 2 and carry over 16.

8
20
40
50
100
125

16
12



2
5

Third Column from Right: 20 + 40+ 16 = 76. Bring down 6 and carry over 7.

8
20
40
50
100
125
7
16
12


6
2
5

Fourth Column from Right: 8 + 7 = 15. Write down 15.

8
20
40
50
100
125
7
16
12

15
6
2
5

This 15,625 is the cube of the number 25.

Further example, 333 =?

Step-1

33
32×3
3×32
33
Worked-out

27
27
27
27
Step-2


54
54

Step-3
Carries
8
8
2

Sum
35
9
3
7

So, the cube of 33 is 35,937.

423 =?                 
Step-1

64
32
16
8
Step-2


64
32

Step-3
Carries
10
4


Sum
74
0
8
8

          So, the cube of 42 is 74,088.

893 =?                 
83
82×9
8×92
93
512
576
648
729

1152
1296

512
1728
1944
729

For convenient addition, you can write the values of each column total placing as many ‘zeros’ after the number as there are column(s) in the right and then add this way:

512000
172800
  19440
      729
704969
So, 893 = 704,969

You can also cube a 3-digit number the same way, considering the first 2 digits as a single digit:

Say, 1033 =?
Step-1

103
102×3
10×32
33
Worked-out

1000
300
90
27
Step-2


600
180

Step-3
Carries
92
27
2

Sum
1092
7
2
7

So, 1033 = 1,092,727




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3 comments

  1. (a+b)^3 formula is being applied here

    ReplyDelete
  2. thank you lenny you idiot. also the 'Shortcut to a cube number' graphic is amazing.

    ReplyDelete

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