The way of find Cube roots using approximation method

I find cube roots using approximation method. For example, 10x10x10=1000; 20x20x20=8000. Therefore, any number between 1000 and 8000 will have cube root between 10 and 20. 

Cube root of 15000 is 10 times cube root of 15 (15x1000)

In general, split the given number in three-digits parts from the right-end.

Take the first part from the left-end. Find the cube root of that number. That gives the first cue to the answer. Then take the next three digits. Look at the unit digit. Cube numbers always end in 1, 8, 7, 4, 5, 6, 3, 2, 9 or 0. The unit digit of the required number is 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 respectively.

This method is very useful for Banking recruitment tests.

Examples:

Perfect cubes:

Find the cube root of 29,791.

Now the first part is 29; the cube root of 27 is 3; therefore, the ten's digit is 3. Remember that you can't take 4 because the cube of 4 is 64, which is greater than 29.

As far the unit digit, it can only be 1. So the number is 31.

Find the cube root of 314,432.

The first part is 314; the cube of just below this number is 216 and its cube root is 6. Therefore, the ten's digit is 6. Now the next part is 432, whose unit digit is 2. Therefore, the unit digit of our required number is 8. So the number is 68.

Cube root of any number:

Find the cube root of 30, 000.

We know this number is not a perfect cube. So our answer will be in decimal.

It can be written as 1000*30; cube root of 1000 is 10. So cube root of the number is 10 times cube root of 30. 30 = 27+3 or 27(1+1/9); cube root of 27 is 3 and cube root of (1+1/9) is (1+1/27) approx or 1.037; therefore, 30*1.037 = 31.11 approx