How to obtain the cube of a number ?

In the previous tutorial on mathematical shortcut, you learnt how easy it is to obtain the square of any number by slightly modifying the formula.As an extension to that shortcut, In this tutorial, we are going to learn how to obtain the cube of a number.

Once you practice this shortcut, you will see, how easy it is to obtain the cube of any 2-digit number and even some 3-digit numbers. In competitive examinations, we might have often come across questions like  973, 873 etc.

In order to use this shortcut, is important that you know the cubes of all the numbers till 10 at least.

Let us recall the cubes of the number till 12.

 

Number Cube
1 1
2 8
3 27
4 64
5 125
6 216
7 343
8 512
9 729
10 1000
11 1331
12 1728

 

I hope you all remember the square formula  :  ( a + b)3 = a3 + 3ab(a + b) + b3

( a + b)3 = a3 + 3a2b + 3ab2 + b3

 

Lets modify the formula to look something like this :

 

Cube_numbers0

 

Let’s understand the shortcut with an example.

Example : Compute  143

 

Cube_numbers1

 

 

 

Step 1 :  Break the number such that a=1, and b=4

Step 2 :  Compute a3, a2b and ab2 and write as shown in the updated formula

Step 3 :   Notice the second row of the formula is obtained by doubling the middle 2-terms of the first row.

Step 4 :   Add the terms. Notice the carry-forward in each step.

Very easy right đŸ™‚

 

Example : Let’s take another example. Let’s say we want to compute  523. In this a=5 and b=2.

 

 

Cube_numbers2

 

Example : Can you try what is 1223 ?

 

Cube_numbers3

 

If you know the cubes of number till 10, you can easily obtain the cubes of all the numbers till 100 using this shortcut.

 

Exercise : On the similar lines, can you calculate,

  • 153
  • 343
  • 673
  • 993
  • 1053

 

Please contact me if some point in the tutorial is not clear. I would be glad to help.

 

Kiran Chandrashekhar

Hey, Thanks for dropping by. My name is Kiran Chandrashekhar. I am a full-time software freelancer. I love Maths and Mathematical Shortcuts. Numbers fascinate me. I will be posting articles on Mathematical Shortcuts, Software Tips, Programming Tips in this website. I love teaching students preparing for various competitive examinations. Read my complete story.

3 Comments

  1. Hey thank you so much… for giving suxh a nic shortcut tricks.. but i have prblm… i understood ur tricks… but i confused… sumtimes while finding main final ans could you pls elaborate me… asap

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