If someone cubed a two-digit number on a calculator and gave you the
result - but not the original number - could you extract the cube root?
With this trick, you'll be able to do just that - instantly!
First, memorize the cubes of the digits 1 through 9:
1 --> 1
2 --> 8
3 --> 27
4 --> 64
5 --> 125
6 --> 216
7 --> 343
8 --> 512
9 --> 729
Next memorize the "endings" of the cubes. For example, the ending of 93 is 9, because 93 = 729. The "ending" (or last digit) is 9.
SAME
1 --> 1
4 --> 4
5 --> 5
6 --> 6
9 --> 9
DIFFERENCE OF TEN
3 --> 7
7 --> 3
2 --> 8
8 --> 2
Now how to do the trick!
Tell a friend to secretly pick any two-digit number and then have him or her use a calculator to cube it. Let's say he picks 76. So using the calculator he computes 76 x 76 x 76 . He then tells you the cube:
438,976.
To instantly determine his original number (ie, compute the cube root), follow these easy steps:
1. Drop the last three digits and find the largest cube contained in 438. This is 73 = 343, so the tens-digit is 7.
(This is why you had to memorize the cubes of the digits 1 through 9)
2. Now go back to the last three digits. Look at the last digit, 6.
That's the same ending as 63, so your units-digit is 6.
(This is why you had to memorize the "endings" of the cubes for digits 1 through 9)
So the cube root of 438,976 is 76
Another example:
Let's say your friend chooses a secret two-digit number whose cube is 79,507. How do you instantly determine the cube root?
1. Drop the last three digits and find the largest cube in 79. This is 43 = 64, so the tens-digit of the cube root is 4.
2. Now go back to the last three digits. Look at the last digit, 7.
That's the same ending as 3-cubed. So the units-digit of your cube rootvis 3.
Therefore, the cube root of 79,507 is 43.
