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Instant Mental Calculation of Cube Roots

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Learn how to mentally calculate cube roots and amaze your friends!

  

Performance

By learning this simple system you will be able to instantly calculate the cube root of the spectator's number.

Ask the spectator to choose any whole number less than 100 and, using a calculator, to find its cube by multiplying the number by itself, then multiplying the answer by the original number.

Alternatively, if the spectator knows how to use scientific calculator, they can enter the original number, then press the "x^y" key followed by 3 and =.

The spectator then calls out the answer, and you instantly reveal the original number (i.e., the cube root).

Note that this method will not work with cubes of numbers greater than 99. Also the method only works when the cube root is a natural number (integer).

    
   
    

Step 1: Learn the Cubes of 0 to 9

To master the system you must learn by heart the cubes of numbers 0 to 9, which are shown in the table below. You also need to consider the last digit of each cube.

NumberCube Last Digit
000
111
28 8
3277
4 644
51255
62166
7343 3
85122
9 7299

Note how the last digit of the cubes for 0, 1, 4, 5, 6, and 9 end with the original number.

Note how the last digits for the cubes of 2 and 8 are swapped.

Note how the last digits for the cubes of 3 and 7 are swapped.


Step 2: Determine the Cube Root

Ignore the last three digits of the number called out by the spectator and choose the memorised cube which is just lower (or equal) to the remaining number. The cube root of this is the first digit of your answer.

Now consider the last digit of the number called out by the spectator. This will indicate the last digit of your answer. For example, if the last digit of the number called out is 3, then the last digit of the cube root is 7 (see the last digit values in the table above).

Examples

Spectator CallsIgnore last 3Lower Cube First DigitLast DigitCube Root
1728111212
2195221828 28
5065350273 737
11764911764 4949
148877148 1255353
216000 2162166060
35791135734371 71
6360566365128 686
830584830729 9494

Step 3: Practice, Practice, Practice !

Before you try this out on your friends, you should practice until you can calculate the cube root instantly and without error. If you can't do this, then practice some more! To practice and assess your ability, you can use the test below.

 
     
 
 
 
 
 
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