Using Mental Arithmetic to determine:
Cube RootsImmediately know the cube-root of of any whole cube from 1 to 1,000,000
The Trick: To determine the cube-root of any whole cube, from one to one million, within a second or two, without any calculator...
1 x 1 x 1 = 1 (cube-root of 1 = 1)
2 x 2 x 2 = 8 (cube-root of 8 = 2)
3 x 3 x 3 = 27 (cube-root of 27 = 3)
4 x 4 x 4 = 64 (cube-root of 64 = 4)
5 x 5 x 5 = 125 (cube-root of 125 = 5)
So what is the cube root of 1,000,000? That's easy. It's 100.
But now, how would you instantaneously determine the cube-root of 493,039 ??
That is, how would you get the cube-root of 493,039, within one or two seconds, without a calculator, without paper, and without any writing implement?
Or, for example, what is the cube-root of 912,673?
Answers:
The cube-root of 493,039 is 79...
The cube-root of 912,673 is 97...
Trust me, you don't have to memorize the cube-roots...
Instead, i will teach you how to do this in your head, instantaneously...
All you have to do is memorize the primary cubes from one to ten:
1 x 1 x 1 = 1 (cube-root of 1 = 1)
2 x 2 x 2 = 8 (cube-root of 8 = 2)
3 x 3 x 3 = 27 (cube-root of 27 = 3)
4 x 4 x 4 = 64 (cube-root of 64 = 4)
5 x 5 x 5 = 125 (cube-root of 125 = 5)
6 x 6 x 6 = 216 (cube-root of 216 = 6)
7 x 7 x 7 = 343 (cube-root of 343 = 7)
8 x 8 x 8 = 512 (cube-root of 512 = 8)
9 x 9 x 9 = 729 (cube-root of 729 = 9)
10 x 10 x 10 = 1,000 (cube-root of 1,000 = 10)...
Now here's how you do it:
First, give a friend a calculator, and ask them to choose any number from 1 to 100, and to use the calculator to cube it...
In one of the above examples, the number 79 was chosen. Cubing it, using a calculator, 79 x 79 x 79 = 493,039...
The person holding the calculator tells you the cube, and your job is to get the cube-root immediately, using "mental arithmetic."
The way you do it is this:
If the large number ends in 1, 9, or 4, 5, or 6... then the cube-root also ends in 1, 9, 4, 5, or 6... If the large number ends in 2 or 3, the cube ends in 8 or 7... If the large number ends in 7 or 8, the cube-root ends in 3 or 2... (see above list of primary cubes)
Let's look at the example above: 79 x 79 x 79 = 493,039
So if i tell you the cube is 493,039, you know immediately that the cube-root ends with a 9...
But how do you determine the rest of the cube-root??...
Since we're only dealing with cubes of numbers from 1 to 99 (while the cube-root of 1,000,000 is 100), we know that the cube-root will be either a 1 or 2-digit number... Anything between 1,000 (the cube of 10) and 1,000,000 (the cube of 100) will be a 2-digit number.
Now, look to the left of the comma in the larger number 493,039. The number is 493... Go back to the list of primary cubes from 1 to 10, and 493 will fit between 7 and 8... The cube-root of 493,039 is thus 79...
Try another: 262,144... The cube ends with a 4, thus the cube-root ends with a 6... The thousands side show 262, which is between 216 (the cube of 6) and 343 (the cube of 7)... Thus, the answer is 64...
With a little practice, it gets very easy... You'll amaze your friends...