Step1: Write numbers in a row of 4 terms in such a way that the first one is the cube of the 1^{st} digit, second one is the square of 1^{st} number multiplied by 2^{nd} digit, third one is the 1^{st} digit multiplied by square of 2^{nd} digit and the fourth one is the cube of the 2^{nd} digit.Step2: Write twice the values of 2nd and 3rd terms under the terms respectively in second row.Step3: Add all the values columnwise and follow the carry over process.
Step1 : 1^{3} 1^{2}×4 1×4^{2} 4^{3}
Workedout row : 1 4 16 64
Step2 : 8 32
Step3 : 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.
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 =?
Step1

2^{3}

2^{2}×5

2×5^{2}

5^{3}


Workedout

8

20

50

125


Step2

40

100


Step3

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, 33^{3} =?
Step1

3^{3}

3^{2}×3

3×3^{2}

3^{3}


Workedout

27

27

27

27


Step2

54

54


Step3

Carries

8

8

2


Sum

35

9

3

7

So, the cube of 33 is
35,937.
42^{3} =?
Step1

64

32

16

8


Step2

64

32


Step3

Carries

10

4


Sum

74

0

8

8

So, the cube of 42 is
74,088.
89^{3} =?
8^{3}

8^{2}×9

8×9^{2}

9^{3}

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,
89^{3} = 704,969
You can also cube a 3digit number the same way, considering the first 2 digits as a single digit:
Say, 103^{3} =?
Step1

10^{3}

10^{2}×3

10×3^{2}

3^{3}


Workedout

1000

300

90

27


Step2

600

180


Step3

Carries

92

27

2


Sum

1092

7

2

7

So, 103^{3} =
1,092,727
(a+b)^3 formula is being applied here
ReplyDeletethank you lenny you idiot. also the 'Shortcut to a cube number' graphic is amazing.
ReplyDeleteFabulous
ReplyDeleteIt is not totally the (a+b)^3 formula though.
ReplyDelete