Take a look at this video of Scott Flansburg on the Discovery Channel’s “More Than Human”:

This trick does require some memorization though, and also requires the

number given to be a perfect cube. You need to memorize the cubes of

the numbers 0 through 9 (or be able to figure them out on the spot).

This information is contained below:

Note

that the last digits of the cubes on the right have all the numbers 1

to 9, but no number is repeated. Here is how to find the two-digit cube

root of a perfect cube.

Take a number, such as 658,503 which is grouped into two parts.

1.

Looking at the number we see it ends in a 3, and according to the table

only 7^3 ends in a 3, thus the last digit of our number is 7.

2.

Next, ignore the last 3 digits of the cube, so consider 658. Compare

these digits with the table above. Note that 658 fits between 512 and

729. You always choose the smaller one, in this case 512 which happens

to correspond to 8^3.

Thus, the last digit is 7 and the first digit is 8, giving an answer of 87.

Normally

this trick is used for six digit perfect cubes. To help understand how

this works, ask yourself – What is the last digit of (10x+y)^3? Clearly

it is y^3 mod 10 (how does this relate to #1?).

Another Example:

In 474,552 we have that 343 is the immediate smallest number from 474 so the first digit is 7.

The last digit in 474,552 is 2 and only 8^3 ends in a 2, so the last digit is 8. Hence, 78^3=474,552.

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