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

Following a few simple steps you will be able to instantly calculate the

fifth rootof 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 non-whole numbers, or with numbers greater than 99.

To master the system you must

learn by heartthe fifth powers of numbers 0 to 9, which are shown in the table below. You also need to consider the last digit of each fifth power.

Number 5th Power Last Digit 0 0 0 1 1 1 2 32 2 3 243 3 4 1024 4 5 3125 5 6 7776 6 7 16807 7 8 32768 8 9 59049 9

Note how the

last digitof every fifth powerends with the original number.

Ignore the last

fivedigits of the number called out by the spectator and choose the memorised fifth power which isjust lower(or equal) to the remaining number. The corresponding fifth root is thefirst digitof your answer.

Now consider the

last digitof the number called out by the spectator. This is thelast digitof your answer (see table above).

## Example 1

Spectator calls 1073741824

- Ignore last five digits = 10737
- Lower (or equal) fifth power = 7776
- Fifth root of 7776 is 6 = first digit of answer
- Last digit of spectator's call is 4 = last digit of answer
- Therefore the fifth root of 1073741824 is 64

## Example 2

Spectator calls 130691232

- Ignore last five digits = 1306
- Lower (or equal) fifth power = 1024
- Fifth root of 1024 is 4 = first digit of answer
- Last digit of spectator's call is 2 = last digit of answer
- Therefore the fifth root of 130691232 is 42

## Further Examples

Called

Fifth

PowerIgnore

Last

FiveLower

(or =)

PowerFirst

Digit

(F)Last

Digit

of CallLast

Digit

(S)Fifth

Root

= FS248832 2 1 1 2 2 12 17210368 172 32 2 8 8 28 69343957 693 243 3 7 7 37 282475249 2824 1024 4 9 9 49 418195493 4181 3125 5 3 3 53 777600000 7776 7776 6 0 0 60 1804229351 18042 16807 7 1 1 71 4704270176 47042 32768 8 6 6 86 7339040224 73390 59049 9 4 4 94

Before you try this out on your friends, you should practice until you can calculate the fifth 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 Fifth Root Tester shown below.

## Fifth Root Tester

## by Psychic Science

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