How to find cube root of a number in less than 5 seconds

Forget about finding cube roots using factors and long division method ! Learn today on how to find a cube root of a number in less than 5 seconds and that too solving them mentally in your head.

Solving for a cube root of a number usually takes about 10 minutes of calculation and most of us usually use the traditional method of finding a cube root using factors method or long division method which is quite tedious but today I will show you how you can solve these monstrous cube roots (no matter how big the number is) in less than 5 seconds. Ready to rumble ? Read on.

Before I start you must remember cubes of numbers from 1 to 10 which are as follows and notice the unit digit of the cubes :

Table -1

1^3 = 0 1 (1 -> 1)
2^3 = 0 8 (2 -> 8)
3^3 = 2 7 (3 -> 7)
4^3 = 6 4 (4 -> 4) ---> (b)
5^3 = 12 5 (5 -> 5)
6^3 = 21 6 (6 -> 6)
7^3 = 34 3 (7 -> 3) ---> (a)
8^3 = 51 2 (8 -> 2)
9^3 = 72 9 (9 -> 9)
10^3 = 100 0 (10 -> 0)

Remember the unit digits for these cube roots where you will notice 2,3 (8,7) and 8,7 (2,3) are complimentary while the remaining have the same unit digit as the cubed number.

Now let's say we want to find the cube root of 103823.. First we will break the number into groups of 3 from the right like this

103 823

Notice the unit digit number of the first group from the right that is 823 . Where for the number 3 we get the compliment number as 7 (please see table 1 , from (a)) and will be the unit digit of our solution.

coming to 103, we have to find the nearest cube to this number which is 64 (please see table 1 , from (b) where we can't take 125 as it exceeds 103) and is cube of 4 , therefore 4 will make the tens digit of our solution and thus.

3v103823 = 47

Q. Let's solve another question for 3v42875
sol: First group them into groups of 3 -> 042 875
Since 875 has unit digit 5 it's cube root number's digit will also be 5 (from table - 1)
Coming to 042 the nearest cube root smaller than this number is 27 which is cube of 3 , thus
3v42875 = 35

Q. Let's solve one more question but this time for a bigger number like 3v160103007
sol: Grouping the numbers into group of 3 ---> 160 103 007
Since 007 has unit digit 7 it's cube root's unit digit will be 3. (from table - 1)
Coming to 103 the nearest cube root smaller than this number is 64 which is cube of 4 , thus
tens place in the cube root will be 4
For 160 the nearest cube root smaller than this number is 125 which is cube of 5 , thus
hundreds place in the cube root will be 5

Therefore 3v160103007 = 543

That's all folks, now you know how to solve cube roots for a number in less than 5 seconds. Much better than finding factors or using long division method, isn't it? However beware that this only applies for perfect cubes and can also be used for irregular cubes to approximate the answer. With a bit of practice you can solve them mentally in your head, no need for pen and paper. :)

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Author: Sarojha13 Jul 2016 Member Level: Gold   Points : 1

Good. But how to find that the number is a perfect cube. For the perfect cube, the method is really good and easy.

Author: Krishna Teja Yeluripati01 Aug 2016 Member Level: Gold   Points : 3

Nice shortcut to find the cube root of a number. This technique sometimes results in approximate cube root only. In case you want to check whether a number is a perfect cube or not i.e. to know whether the result of this technique is a perfect cube root or not, this is the technique.
1) Calculate the digital root of the number. The digital root of a number is the number obtained by adding sum of digits of a number repeatedly until a single digit number is obtained. Consider 67899 for example. Its digital root is calculated as follows.
6+7+8+9+9=(39) i.e. Not single digit. So, continue
3+9=(12) i.e. Not single digit. So, continue
1+2=(3) i.e. 3 is the digital root of 67899.
2) If the digital root is one of the numbers 1, 8, 9 we can say that the given number is a perfect cube.

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