How to obtain the cube root of a perfect cube?

 

In this tutorial, we are going to learn the Mathematical shortcut to obtain the cube root of any perfect cube

Once you practice this shortcut, no matter how big the number is, you can easily tell the square-root of the number.  Please note, this shortcut works only with perfect cubes.

The tutorial How to obtain the square roots of a perfect square?, explains how to obtain the square roots of any perfect square in less 10 seconds.

Before we go into this shortcut, it is very important that we know the cubes of the number atleast till 10. Let’s recall the cubes of the number till 10

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

 

Notice the unit-digits of the cube numbers.

  • If the perfect cube ends with 1,4,5,6,9,0  the unit digit of cube root will respectively be 1,5,6,9,0.
  • If the perfect cube ends with 2, the unit digit of cube root will end with 8 and vice-versa.
  • If the perfect cube ends with 3, the unit digit of cube root will end with 7 and vice-versa.

 

Last Digit of the Cube

Last Digit of the cube root

1

1

2

8

3

7

4

4

5

5

6

6

7

3

8

2

9

9

0

0

Please note, that this shortcut will only for perfect cubes. Let’s try to understand the shortcut through an example.

 

Exercise : Let’s compute the cube-root of the perfect cube of 54872.

Step 1:  Irrespective of how big the number is, group the number such that, the last 3 numbers is in 1 group and rest of the digit in another group. So, we have 54 and 872.

Step 2: Look at the unit digit of 872. So if the unit digit is 2, the cube-root will have a unit digit of 8. This is explained in the table.

Step 3: Now consider the first part 54. It lies between the perfect cube 27 and 64 whose cube roots are 3 and 4 respectively. Now, choose the lowest cube-root which is 3 in this case.

So the cube root is 32.

 

Exercise : Let’s take up another example. Let’s compute the cube-root 1157625.

Solution :

Let’s compute the cube-root of the perfect cube of 1157625.

Step 1 : As explained in the shortcut, first step is to break the number into 2 parts. 1157 and 625.

Step 2 : Consider the last part 625. Since the unit digit is 5, the cube-root will also have a unit digit of 5.

Step 3 : Now consider the first part 1157. It lies between the perfect cubes 1000 and 1331 whose cube roots are 10 and 11 respectively. Take the smallest cube-root which is 10 in this case.

So the cube root is 105.

 

On the similar lines, can you obtain the cube roots of,

  • 970299
  • 421875
  • 405244
  • 884736

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. Helpful information. Lucky me I found your site by chance, and I am stunned why this coincidence did not took place earlier! I bookmarked it.

  2. Thank for the trick….
    What if the figure is of more than 6 digits?
    Like… 1404928….

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