Long ago you had to find square roots the long way. You know, group the digits in pairs, find the nearest root for the first one or two digits. Multiply it by 20 and use that number to divide into the difference plus the next two digits (or something similar, I forget).

Now, thanks to Ray Wade and Bill Edmondson, and Bill's book "Math Magic" you can learn the secrets of finding cube root! Two methods are given in the book.

The easy way to find cube roots is to only solve problems with exact cube roots. This is also the way to learn how to solve more difficult problems. Use or memorize the chart below:
 

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

You can use this chart three ways: (1) to solve simple problems, (2) to find the first digit when dealing with larger problems, (3) to find the last digit for exact root large problems, and (4) to estimate other roots.

(1) Examples of the first way would be "The cube root of 125 is 5."

(2) For the second way, group large numbers in threes, starting from the right. 456,533 is already grouped for finding cube root by the commas! Look at the chart and find where 456 would fit: somewhere between 343 and 512, so the 1st digit of the root would be a "7".

(3) Look again at the chart again, and notice that the last digits of the cubes are all different . If 456,533 is an exact cube, the "ones" digit of 3 indicates that the cube root of 343 = 7. Therefore the answer should be 77x77x77 = 456,533. Check it and see.

(4) 45,118,016 is already grouped for finding cube root by the commas. Look at the chart and find where 45 would fit: somewhere between 27 and 64, so the 1st digit of the root would be a "3".

(5) Now look again at the chart, and find an answer ending in 6. If 45,118,016 is an exact cube, the "ones" digit of 6 indicates that the cube root of 216 = 6 gives the third digit of your answer.

(6) The final answer will lie between 306 and 396. Make a guess, say 346, and look for your calculator. Assuming it doesn't have a y cubed key, multiply 346 x 346 x 346. Not quite big enough was it? Repeat with 356. Aha!

A good party exercise would be to print out the cubes, pass them out, and make a contest of mentally solving 2-digit-answer cubes. More experienced cubists might try 3-digit dudes! Notice that cubes of one digit numbers are the same as the digit for 6 digits, and 7 & 3 swap places (7-cubed ends in 3 and vice versa) and 2 & 8 swap places. This secret can speed memorization.

If you want to learn the cube root equivalent of the square root method, you may be disappointed. The cube root method only approximates the answer, and is not exact like SQRT. The Old Ones used LOGARITHMS, and divided the log by 3 to get cube roots.

My friend Durwood has explored both cube root methods, and is also a master of the calendar: He can tell the day of the week you were born on when you tell him your birthday. I'm trying to persuade him to present a program soon, to coach budding math-magicians and entertain the math-potatoes.

6/2000 update: Durwood continues to practice cube roots, working on finding the THREE-Digit cube of NINE-Digit numbers. He's working on the proportions for different size numbers, and hit three in a row exactly the other day!