Here is a trick I learned several months ago. With this method, you can cube root any whole cube number less than 7 digits long in seconds.

Difficulty: Can be very difficult or easy depending on how good you are at maths.

^3 means cubed. 4^3 = 4 * 4 * 4 = 64. Multiplying a number by itself three times. Cube root of 64 is 4. Cube root is reversing this procedure (not dividing).

First of all, learn the first 10 cube numbers.
1 cubed = 1.
2 cubed = 8.
3 cubed = 27.
4 cubed = 64.
5 cubed = 125.
6 cubed = 216.
7 cubed = 343.
8 cubed = 512.
9 cubed = 729.
10 cubed = 1000.

Once you have done that, look at any cube number.
E.g. 72^3 = 373248.

You look at the last digit of the cube number, it is 8. So you look at which cube number between 1 to 10 ends with an 8. 2 cubed ends with 8. So the cube root of 373248 ends with a 2.

Then you ignore the last 3 digits of 373248, and you are left with 373. You look at the biggest cube number that could fit 373, 7^3 = 343, fits in. However, 8^3 = 512 does not fit in. So this means the number starts with a 7.

So therefore, the cube root of 363247 is 72.

Another example.
13 ^ 3 = 2197. It ends with a 7, and 3 cubed ends with a 7. Therefore the cube root of 2197 ends with a 7. Ignore the last three digits of 2197, you are left with 2. The biggest cube number that fits into to is 1^3. 2^3 = 8 is too big. So the number starts with a 1.

Therefore, the cube root of 2197 is 13.

Only works with whole cube numbers, hope it is easy to understand,
Da Man.

That's awesome!! I never thought of that, this will help me in class, btw how do u know all these shortcuts?

Dude this is so amazing! I'm going to impress my Trigonometry teacher with this, lol.

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Wow, this is an excellent trick. It makes solving for cube roots a whole lot easier without the need of a calculator.

I didnt understand this... I didnt learn it yet probally because im only in 4th grade.

Very helpful thanks :)

Edit after a few days : This trick is really fun, but I must correct you on one point :P
You can also use it on decimal numbers which only have one tail and are smaller then 10.

For example if you want the cube root of 195.112.
You take the last number, which is 2, and look which cubes number has a 2 in the end, which is 8.
So the last digit of the cube root is 8.
Take out the last three numbers and you have 195 left, the cube of 5 ( 125 ) is the closest one. So the first number is 5, the last is 8, which makes it 5.8 :)

You could also use it with numbers above 10 with one tail but you would need to know the cube of 11, 12 and so forth.

Had fun playing with it, thanks :D

Woah! I never thought that there could be a shortcut like this for doing cubed roots!

woah thats awsome

yay Da man. this really helped me... Thanks for the help XD lol...

wow, this is awesome O.o this should help me quite a bit on the PSAT and SAT

this trick is awesome I would likely try it but maybe when I have time to lazy to study the cube root pattern

very helpful thread it helped me alot thanks da man for such an amazing thread :D

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lol LT.
But it is really awesome.
I find this technique really good.
Gonna use this this trick in my math problems.
Thanks for this trick Da Man :D