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# Instant Mental Calculation of Fifth Roots

## Performance

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

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

Alternatively, if the spectator knows how to use scientific calculator, they can enter the original number, then press the "x^y" key followed by 5 and =.

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

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

## Step 1: Learn the Fifth Powers of 0 to 9

To master the system you must learn by heart the 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 Fifth 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 digit of every fifth power ends with the original number.

## Step 2: Determine the Fifth Root

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

Now consider the last digit of the number called out by the spectator. This is the last digit of your answer (see table above).

### Examples

 Spectator Calls Ignore last 5 Lower 5th Power First Digit Last Digit Fifth Root 248832 2 1 1 2 12 17210368 172 32 2 8 28 69343957 693 243 3 7 37 282475249 2824 1024 4 9 49 418195493 4181 3125 5 3 53 777600000 7776 7776 6 0 60 1804229351 18042 16807 7 1 71 4704270176 47042 32768 8 6 86 7339040224 73390 59049 9 4 94

## Step 3: Practice, Practice, Practice!

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 test below.