Posted by: catindiaonline | October 25, 2008

How to Do Cube Roots of 9 Digit Numbers in Your Head

What is a Cube Root?

(Just in case you don’t already know.) A number cubed is that number times itself times itself. For example, 4 cubed, normally written 43, is 4 × 4 × 4 = 64. The cube root goes in the opposite direction, so the cube root of 64 is 4.

To give a larger example, 657 cubed = 6573 = 657 × 657 × 657 = 283593393, so the cube root of 283593393 is 657.

Doing it in your head

Now I’ll have to admit that I used a calculator to calculate that 6573 = 283593393 (actually I’m lying – I did it in Python, but that’s beside the point). But I am claiming that you can learn to calculate the cube root of numbers like 283593393, by mental arithmetic alone.

First Cheat

When I say “the cube root of numbers like 283593393”, there is of course something special about 283593393, which is that it is a cube of a whole number, so it’s cube root is a whole number. Although there are 999999999 numbers up to 9 digits long, only 999 of these numbers have cube roots that are whole numbers.

But if you are giving a display of your mental arithmetic powers to an audience, this is no problem. Give someone in your audience a calculator. Tell them to think of a 3 digit number, multiply it by itself twice and tell you the answer (which will be 7 to 9 digits long). You will then tell them what the original number was. Don’t ask them to supply a random 9 digit number, because a random 9 digit number probably won’t be a cube of a whole number, and you will be in trouble, and the following strategies won’t work.

Cube Roots up to 3 Digits

If you had to calculate the cube root of a 3 digit number, it would be quite easy. Here is a table of cubes from 1 to 10:

n n3
1 1
2 8
3 27
4 64
5 125
6 216
7 343
8 512
9 729
10 1000

To do cube roots of 9 digit numbers, you are going to have to be familiar with these first 10 cubes. So you might as well memorise them. And if you have memorised them, then there isn’t really any trick to calculating the cube roots.

For rest go to CAT India Online’s CATclub



  1. u r doing a gud job man…it’s really going to help CAT aspirants

  2. this is use full for all

  3. Great , Most Useful Thing For Accounting.

  4. GREAT,

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