Find Cube Root Of Any Number In 5 Seconds

Find Cube Root In 5 Seconds
Find Cube Root In 5 Seconds

Finding cube root of a number gives us pain sometimes and that pain forces us to dream about a calculator. What if you are in an examination hall and the exam body have a restriction for using a calculator. And you have to find the cube root of say 328,509. As the title of this post suggest that we will show you a method to find the cube root in your mind in just 5 seconds so let’s get started.

To Find Cube Root In 5 Seconds

To find the cube roots you first need to remember the cube root of numbers 1 to 10. Most of us can quickly produce the cube roots of 1 to 10 still if have trouble reproducing by simple mental multiplication. Here is the list.

13=1, 23=8, 33=27, 43=64, 53=125, 63=216, 73=343, 83=512, 93=729, 103=1000

Now take a close look at the last digit of cube’s in the table.

Number Cube Last Digit Remarks
1 1 1 same
2 8 8 2 –> 8
3 27 7 3 –> 7
4 64 4 Same
5 125 5 Same
6 216 6 Same
7 343 3 7 –> 3
8 512 2 8 –> 2
9 729 9 Same
10 1000 0 same

Now remember this:  28 , 8⟹2 , 37 and 7⟹3 that’s it with an example we will show the method

Example 1: Find the Cube root of  328,509?

Group the number from back in the pack of 3 (cube ~ 3) i.e. 328 509
The last digit of 509 is 9 and from the above table 9 => 9
Now the number (remaining) 328 lies between cube root of 6 (216) and 7 (343). Take the lowest number i.e 6
Hence the cube root of 328,509 is 69

To be more clear, let’s calculate the cube root of 5,832

Group the given number: 5  832
The last digit of 832 is 2 , from above table 2 –> 8
Remaining digit: 5 , lies between cube of 1 (1) and 2 (8). Take the lowest number i.e 1
Hence the cube root of 5,832 is 18

Ok, Not yet convinced that you can Calculate the cube root in 5 seconds. Here is another example.
Calculate the cube root of 389,017 in 5 seconds

Find IBPS Clerk Syllabus here
Group the given number: 389  017
The last digit of 017 is 7 , from above table 7 –> 3
Remaining digit: 389 , lies between cube of 7 (343) and 8 (512). Take the lowest number i.e 7
Hence the cube root of 389,017 is 73

NOTE: This method works very well only for perfect cubes and for numbers between 0 to 99 for number greater than 100 it can take more than 5 seconds

The Mind Game of Cube Root In 5 seconds:

Using the above method you can play a mind game with your friends convincing them that you can read there mind. To do so ask you friend to pick (in mind) a number between 0 – 99, tell them to cube the number ( also ask them to keep the number and the cube secret that’s the whole point of this game as in the last you are going to disclose the number initially picked by your friend). Ask  him/her (your friend)  to group the cube in three from the back  at this stage let them reveal the last digit of the cube. If the last digit is 1 –>1,  2 –>8…… and 9 –>9. Now let the reveal the remaining digits. In your  find the lower cube which is closest to remaining digits. That’s it now you have the number picked by your friend at the beginning of the game.

Find the cube root of 33076161 using this method
Grouping it gives: 33076 161
The last digit of 161 is 1. Therefore, the last digit of the cube root is 1
for 33076 lies between cube of 32 (33076) and 33 (33768)
Ok, I know I have told you earlier that you just need to remember cube of 1 to 10 only and now you are thinking how come I have directly written the cube of 32 and 33. You can do that too just look at the number 33076 and find its root by the same method
So, the cube root of 33076161 is  321

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