Find Cube of a two digit number
Example 1 : Find Cube of a two digit number : 14.
1. Find the ratio of the two digits i.e. 1:4
2. Now write the cube of the first digit of the number i.e. 1 x 1 x 1
3. Now write numbers in a row of 4 terms in such a way that the first one is the cube of the first digit and remaining three are obtained in a geometric progression with common ratio as the ratio of the original two digits (i.e. 1:4) i.e. the row is 1 4 16 64
4. Write twice the values of 2nd and 3rd terms under the terms respectively in second row.
1 4
16 64
8
32 (2 x 4 = 8, 2 x
16 = 32)
5. Add the numbers column wise
and follow carry over process. First Column from Right: Bring down 4 and carry over 6
1 4
16 64
8
32
64
6. Second Column from Right: 16 + 32 + 6 = 54 . Bring down 4 and carry
over 5
1 4
16 64
8
32
54 4
1 4
16 64
8
32
17 4 4
8. Fourth Column from Right: 1+1 =2. Write down 2
1 4
16 64
8
32
2 7 4 4
This 2744 is
the cube of the number 14
Example 2 :
Find Cube of a two digit number : 33. (Numbers are same)
i) Find the
ratio of the two digits 3:3 gives 1:1
ii) Now write
the cube of the first digit of the number i.e. 3 x 3
iii) Now write numbers in a row of 4 terms in such
a way that the first one is the cube of the first digit and remaining three are
obtained in a geometric progression with common ratio as the ratio of the
original two digits (i.e. 1:1) i.e. the row is 27 27 27 27
iv) Write twice the values
of 2nd and 3rd terms under the terms respectively in 2nd row. (2 x 27 = 54)
27 27
27 27
54 54
v) Add the numbers column
wise and follow carry over process. First Column from Right : Bring down 7 as it
is and carry over 2
27 27
27 27
54 54
27
vi) Second Column from right:
27+54+2 = 83 write down 3 and carry over 8.
27 27
27 27
54
54
83 27
vii) Third Column from Right: 27 + 54 + 8 = 89 write down 9 and
carry over 8
27 27
27 27
54
54
89 3
27
viii) Fourth Column from Right: 27 +8 = 35, write down 35
27 27
27 27
54
54
35 9 3
27
(This 35937 is the cube of the number 33 )
Find Cube of a 2 , 3 or
4 digit number
Example 1 :
Find Cube of a 3 digit number : To find
cube of 106.
i) The base is
100 and excess is 6.
In this context we double the excess and then add. i.e.
106 + 12 = 118. ( 2 x 6 =12 )
This becomes
the left - hand - most portion of the cube. i.e. 1063 = 118 / - - - -
ii) Multiply
the new excess by the initial excess i.e. 18 x 6 = 108 (excess of 118 is 18)
iii) The last portion of the product is cube of
the initial excess. i.e. 63 = 216.16 in the last portion and 2 carried over.i.e. cube of 106 = 118 / 108 / 2 16 = 1191016.
Example 2: Find the cube of 998.
Base =
1000; initial deficit = - 2.
Cube of 998 = (998 -
[2 x 2]) / (- 6 x - 2) / (- 2)3
___
= 994 / 012 /
008 (1 is carry from 012 to right and 1000 - 008)
Removing the bar number
= 994 / 011 / (1000 - 008)
= 994 / 011 / 992 = 994011992.
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