How to Find Cube Of A Number

Posted on June 2, 2012 by Smruti Shetty

We have learned how to find square of a number, now we will learn how to find the cube of any number.
Finding Cube of a number from 1 to 10 is easy. I will explain here how to find cube of two digit numbers starting from cube of 11.

Cubes of numbers from 1 to 10

{1^3}= 1
{2^3}= 8
{3^3}= 27
{4^3}= 64
{5^3}= 125
{6^3}= 216
{7^3}= 343
{8^3}= 512
{9^3}= 729
{10^3}= 1000

Let us find cube of number from 11 to 30.

Take number ab.
Step1: Find the cube of first digit {a^3}= w

Step2: Write four numbers starting with cube of the first digit in the geometrical ratio in exact proportion of original number.

\text{w x y z such that } \dfrac{a}{b} = \dfrac{w}{x}= \dfrac{x}{y}=\dfrac{y}{z}

Step3: Under second and third number write double those numbers respectively.
\text{w\qquad x\qquad y\qquad z ------------------------1}
         \text{ 2x \qquad 2y \qquad ------------------------2}
\text{-------------------------------------------------}
Step4: Add 1 and 2 to get final result.

Let us take an example to explain the steps to find cube of a number.
Example: {12^3}
Step1: Find cube of 1, {1^3}= 1
Step2: Write four numbers starting with cube of the first digit in the geometrical ratio exact proportion of original number.
1 2 4 8 (original ratio 1/2 = 1/2= 4/2= 8/4)
Step3: Under second and third number write double those numbers
\text{1\qquad 2\qquad 4\qquad 8\qquad -----------------1}
         \text{4\qquad 8\qquad \qquad -----------------2}
\text{-------------------------------------------------}
         \text{1\qquad 7\qquad 2\qquad 8\qquad }

Step4: Add 1 and 2 to get answer {12^3}= 1728

Let us take one more example {22^3}

Step1: {2^3}= 8
Step2: 8 8 8 8 (2/2= 8/8= 8/8= 8/8)
Step3: and Step4: \text{8\qquad 8\qquad 8\qquad 8\qquad -----------------1}
                                       \text{16\qquad 16\qquad -----------------2}
\text{-------------------------------------------------}
                                 \text{10\qquad 6\qquad 4\qquad 8\qquad }
Answer {22^3}= 10648

Practice:
1) {13^3}
2) {24^3}
3) {31^3} (Four numbers in geometric ratio of 3:1 are 27: 9: 3: 1)
4){46^3}
5) {19^3}

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3 Responses to How to Find Cube Of A Number

  1. Asif says:
    July 10, 2012 at 5:50 am

    what is the method to find out the cube of 88,222,6666….etc. ?

    Reply

  2. Pingback: Fast Maths Trick of Calculation | Learning Jigsaw