Here's a fun math secret one can do with their friends to convince them
that you are a human calculator. When in fact, the method behind the
calculation is quite simple. First, ask a friend to pick a two digit
number and cube it. For example, suppose the volunteer selects 52. He
cubes the number to get 52 times 52 times 52 equals 140,608. Then ask
the volunteer to give the number. Very quickly and almost instantly with
practice, you can say that the cube root is 52. How is this done?

First you must know the cubes from 1 to 10. The first 10 cubes are 1, 8,
27, 64, 125, 216, 343, 512, 729, 1000. Now that you know the first 10
cubes, here is the method.

Look at the magnitude of the
thousands digits. Since the number is 140,608, the thousands digits are
140. Now think of what the cube root of 140 is. We know it's between 5
and 6 since 5 cubed is 125 and 6 cubed is 216. So the first number in
the answer is 5. Now look at the last number, which is 8. All we do is
see which cube ends in 8. See that 2 cubed is 8 so the answer is 52.
Notice the cubes from 1 to 10 end in the numbers 0 through 9, no number
is repeated twice. There lies the key to solving these cube roots.

Let's try another example. What is the cube root of 54,872? The
thousands digits in this problem are 54. We know the cube root of 54
falls between 3 and 4 since 3 cubed is 27 and 4 cubed is 64. So we know
the answer starts with 3. Next look at the last number, which is 2.
Which of the first ten cubes end in 2? Looking at the list, 8 cubed is
512, so 8 is the last number. Therefore, the answer is 38.

Note that this method will not work unless the cube root is a whole number.

Over my years of tutoring math, I have used these tricks that I have learned with my students.

Practice calculating cube roots in this fashion and you can wow your
friends. Even if you are not particularly a math wizard, you will appear
to be one.

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