TO FIND CUBE ROOT(short cut method)

 This technique helps you find out the cube root of a  4 or 5 or 6 digits number mentally.

Before going further on the method to find the cube root , please make a note of the following points –

1) Cube of a 2-digit number will have at max 6 digits (99^3 = 970,299). That implies if you are given with a 6 digit number, its cube root will have 2 digits.

2) This trick works only for perfect cubes, it will not work for any arbitrary 6-digit

3) It works only for integers

Now let us start with the trick to cube root of a 5 or 6 digit number in vedic mathematic way.
Say you have to find the cube root of 54872. It is known that it’s a perfect cube.

Now divide this number into two parts. The right hand side should always have 3 digits. Remaining digits will
come in left hand side. Do it as shown below.
54            |             872

You know the answer will have 2 digits. Digit at tens place and digit at units place. We will get the digit at tens place using the left hand side of the original number (54) and digit at units place using right hand side of the number (872)

Step 1.
Memorize these tables (very soon you will know why) –


Table 1: Cube of 1 to 10

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

Table 2: Unit’s digit of Cube Roots

Cube Ends in	Cube Root Ends in
1	1
2	8
3	7
4	4
5	5
6	6
7	3
8	2
9	9
0	0

Step 2.
For left hand side we need to use table 1. We have to see between which 2 numbers in the 2^nd column do 54 lies. In this case it lies between 27 and 64. So we will take the cube root of the smaller number i.e. 27 which is 3.

So 3 is the tens digit of the answer.


Step 3.
For right hand side we need to use table 2. Since our original number (the perfect cube) ends in 2 (see 54872), its cube root will ends in 8.
Thus the units digit will be 8.
Combining the results we get the answer as 38.
Thus (54872)^1/3  =  38

Try for perfect cubes like 185193, 42875, 1728.