Tuesday, 2 May 2017

What Is The Cube Formula And How to Find Cube Of A Number

Cube Formula

Since we have earlier discussed how to find squares and how to find square root of any number, the next concept to understand is what is cube and cube formula and how to find the cube of a number easily. 


What Is Cube Of x

Cube is the product of a number multiplied by its square, represented by a superscript figure 3. Hence, cube of x is nothing but square of x multiplied by x.


Cube Formula

cube formula

Things To Remember To Find Cube Of A Number

To find cube of any number, it is of utmost importance that you know the cubes of numbers from 1 to 15 at the tip of your fingers.
cube formula
An interesting thing to notice is how the units place for the cube changes as the units place for the number changes. This would be helpful in finding out cube roots of a number. 
cube formula

  1. When perfect cubes end with, 1, 4, 5, 6, 9 and multiples of 0, the cube root also ends with 1, 4, 5, 6, 9, and 0 respectively
  2. Perfect cubes ending with 2 form complimentary pair with perfect cubes ending with 8. Which means, if a number is ending with 8, the cube root ends with 2. And when a number ends with 2, the cube root ends with 8
  3. Similarly, perfect cubes ending with 3 are also complimentary in nature with perfect cubes ending with 7. Which means, if a number is ending with 7, the cube root ends with 3. And when a number ends with 3, the cube root ends with 7.

How To Find Cubes Of Numbers More Than 15

Method 1: Conventional Method
cube formula
Since it is easier to find out square of any given number, we can then multiply the result with the number itself to get the cube of the number.

Method 2: Smart Method
This method has been taken from vedic math. However, it might not always be easy to apply this method. 

Example 1: Find 243
Solution:

Step1: If we need to find the cube of a 2 digit number, first find the ratio between the 2 digits.
Ratio between the 2 digits is 2:4 = 1:2

Step 2:
In the next step, we must first write the cube of the first digit
23 = 8 _ _ _

Then, we must fill out the next 3 digits in a way that the ratio between 2 consecutive numbers is the same as the ratio we found in Step 1
8 16 32 64

It can be observed that 64 is the cube of the number in unit’s place
43 = 64

This is the best way to verify if we did the ratio correctly. The last number must always be the cube of the number in the unit’s place.

Step 3:
The next step is to double the numbers in between:
16*2=32 
32*2=64
Step 4:
This is a little tricky. Please pay attention.
16 32 64
32 64

We must now add these two numbers, in a way that only one number is taken down in the solution and the rest is carried forward in each vertical column.
cube formula
We must remember that this method can be easily applied only when we have an easy ratio to write out. In this case, 1:2 is the simplest ratio to write out. However, such may not be the case always.

From an exam's point of view, it is wise to practice both these methods to ensure you waste no time in finding cubes of number, irrespective of what the number is.

Let us put your practice to test:

Question 1: Find 323
Question 2: Find 673

Please write your answers in the comments below and tell us which one of these methods you followed to solve these questions and how long it took you to find the answers.
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