Cube of Negative Numbers

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Cube of negative numbers :
In the earlier section, we have learned about cubes of natural numbers. We have seen that the cubes of natural numbers are also natural numbers. Now, we shall learn about cube of negative numbers.

We have, (-1)3 = -1 x -1 x -1 = -1.
:. -1 is the cube of itself.

Similarly, (-2)3 = -2 x -2 x -2 = -8.
:. -8 is the cube of -2.

In general, if m is a positive integer, then (-m)3 = -m x –m x –m = -m3
Thus, for any positive integer, -m3 is the cube of –m.
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Examples :

1) Show that -1331 is a perfect cube. What is the number whose cube is -1331?

Solution :
Resolving 1331 into prime factors, we get
1331 = 11 x 11 x 11
Grouping the factors in triples of equal factors, we get
1331 = {11 x 11 x 11 }
So, 1331 can be grouped into triples so it is a perfect cube of 11.
We know that -m3 is the cube of -m for any positive integer m.
∴ (-11)3 = -1331
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2) Show that -3888 is a perfect-cube. What is the number whose cube is -3888?

Solution:
Resolving 3888 into prime factors, we get
3888 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3
Grouping the factors in triples of equal factors, we get
1331 = {2 x 2 x 2 } x 2 {3 x 3 x 3} x 3 x 3
So, 3888 can not be grouped into triples so it is a not a perfect cube .


Cube and Cube Roots

Cube of Numbers
Perfect-Cube
Properties of Cube
Column method
Negative numbers-cube
Cube-Rational numbers
Cube Root
Finding cube root by Prime Factorization
Cube root of Rational numbers
Estimating cube root

From cube of negative numbers to Exponents

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