Instantly Calculate Cube Roots

Cube Root Calculation

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

Following a few simple steps you will be able to instantly calculate the cube root of the spectator's freely-chosen number.

To Start

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.

Note that this method will NOT work with non-whole numbers, or with numbers greater than 99.

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).

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.

Number	Cube	Last Digit
0	0	0
1	1	1
2	8	8
3	27	7
4	64	4
5	125	5
6	216	6
7	343	3
8	512	2
9	729	9

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).

Example 1

Spectator calls 185193

• Ignore last three digits = 185
  
  
• Lower (or equal) cube = 125
  
  
• Cube root of 125 is 5 = first digit of answer
  
  
• Last digit of spectator's call = 3
  
  
• From table of cubes (shown above), when the last digit of cube is 3, the last digit of the cube root is 7
  
  
• Therefore the cube root of 185193 is 57

Example 2

Spectator calls 438976

• Ignore last three digits = 438
  
  
• Lower (or equal) cube = 343
  
  
• Cube root of 343 is 7 = first digit of answer
  
  
• Last digit of spectator's call = 6
  
  
• From table of cubes (shown above), when the last digit of cube is 6, the last digit of the cube root is also 6
  
  
• Therefore the cube root of 438976 is 76

Further Examples

Called Cube	Ignore Last Three	Lower (or =) Cube	First Digit (F)	Last Digit of Call	Last Digit (S)	Cube Root = FS
1728	1	1	1	8	2	12
21952	21	8	2	2	8	28
50653	50	27	3	3	7	37
117649	117	64	4	9	9	49
148877	148	125	5	7	3	53
216000	216	216	6	0	0	60
357911	357	343	7	1	1	71
636056	636	512	8	6	6	86
830584	830	729	9	4	4	94

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 Cube Root Tester shown below.

Cube Root Tester by Psychic Science