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:
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.
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.
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.
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?).
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.