Cube by Column method
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For finding the cube by column method use the following formula:-
(a + b)
^{3} = a
^{3} + 3a
^{2}b + 3ab
^{2} + b
^{3}
In this method, first find the 2 digits of a number.
Example: 1) 32
^{3}, so here the two digits are 3 and 2.
2) 46
^{3}, two digits are 4 and 6.
Examples:-
1) Find 24
^{3}.
Solution: Here two digits are 2 and 4.
a = 2, and b = 4.
By using the column-method:-
Column I |
Column II |
Column III |
Column IV |
a^{3} |
3 x a^{2} x b |
3 x a x b^{2} |
b^{3} |
2^{3} = 8 + 5 |
3 x 2^{2} x 4 = 48 + 10 |
3 x 2 x 4^{2} = 96 + 6 |
4^{3} = 64 |
13 |
58 |
102 |
4 |
13 |
8 |
2 |
4 |
∴ 24
^{3} = 13824
_________________________________________________________________
2) Find 42
^{3}.
Solution: Here two digits are 4 and 2.
a = 4, and b = 2.
By using the column-method:-
Column I |
Column II |
Column III |
Column IV |
a^{3} |
3 x a^{2} x b |
3 x a x b^{2} |
b^{3} |
4^{3} = 64 + 10 |
3 x 4^{2} x 2 = 96 + 4 |
3 x 4 x 2^{2} = 48 + 0 |
2^{3} = 8 |
74 |
100 |
48 |
8 |
74 |
0 |
8 |
8 |
∴ 42
^{3} = 74088
Cube - Cube Roots
• Cube of Numbers
• Perfect- Cube
• Properties of - Cube
• Cube by Column method
• Negative numbers-cube
• Cube - of Rational numbers
• Cube-Root
• Finding cube-root by Prime Factorization
• Cube-root of Rational numbers
• Estimating cube-root
From column method to Exponents
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