Learn instant mental calculation of fifth roots

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

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.

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.

Instant Mental Calculation of Fifth Roots

Performance

Step 1: Learn the Fifth Powers of 0 to 9

Step 2: Determine the Fifth Root

Examples

Step 3: PRACTICE, PRACTICE, PRACTICE!!