# Fifth Root

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### What is a fifth root?

The fifth root of a number is the number that would have to be multiplied by itself 5 times to get the original number.
For example, the fifth root of 243 is 3 as 3 x 3 x 3 x 3 x 3 is 243.
The fifth root of 1,024 is 4, as 4 x 4 x 4 x 4 x 4 is 1,024.

### How to calculate fifth root

Even for perfect fifth root numbers, fifth root can be difficult to calculate by hand.
The most basic techniques involve trial and error.
Example:
Find the fifth root of 32,768
1) Try a number – 5 : 5 x 5 x 5 x 5 x 5 = 3,125 (too low)
2) Try another number that is more than 5 – 6 : 6 x 6 x 6 x 6 x 6 = 7,776(too low)
3) Try a number that is more than 6 – 10 – 10 x 10 x 10 x 10 x 10 = 100,000 (too high)
4) Try a number in between 6 and 10 – 8 – 8 x 8 x 8 x 8 x 8 = 32,768 (answer)
A fifth root can also be calculated as the same number to the exponent 1/5.
5√number = number1/5

### Table – Fifth Root (5√) of 1 – 100

 Fifth root of 0 (5√0) = 0 Fifth root of 1 (5√1) = 1 Fifth root of 2 (5√2) = 1.1487 Fifth root of 3 (5√3) = 1.24573 Fifth root of 4 (5√4) = 1.31951 Fifth root of 5 (5√5) = 1.37973 Fifth root of 6 (5√6) = 1.43097 Fifth root of 7 (5√7) = 1.47577 Fifth root of 8 (5√8) = 1.51572 Fifth root of 9 (5√9) = 1.55185 Fifth root of 10 (5√10) = 1.58489 Fifth root of 11 (5√11) = 1.61539 Fifth root of 12 (5√12) = 1.64375 Fifth root of 13 (5√13) = 1.67028 Fifth root of 14 (5√14) = 1.69522 Fifth root of 15 (5√15) = 1.71877 Fifth root of 16 (5√16) = 1.7411 Fifth root of 17 (5√17) = 1.76234 Fifth root of 18 (5√18) = 1.7826 Fifth root of 19 (5√19) = 1.80198 Fifth root of 20 (5√20) = 1.82056 Fifth root of 21 (5√21) = 1.83842 Fifth root of 22 (5√22) = 1.8556 Fifth root of 23 (5√23) = 1.87217 Fifth root of 24 (5√24) = 1.88818 Fifth root of 25 (5√25) = 1.90365 Fifth root of 26 (5√26) = 1.91865 Fifth root of 27 (5√27) = 1.93318 Fifth root of 28 (5√28) = 1.94729 Fifth root of 29 (5√29) = 1.96101 Fifth root of 30 (5√30) = 1.97435 Fifth root of 31 (5√31) = 1.98734 Fifth root of 32 (5√32) = 2 Fifth root of 33 (5√33) = 2.01235 Fifth root of 34 (5√34) = 2.0244 Fifth root of 35 (5√35) = 2.03617 Fifth root of 36 (5√36) = 2.04767 Fifth root of 37 (5√37) = 2.05892 Fifth root of 38 (5√38) = 2.06994 Fifth root of 39 (5√39) = 2.08072 Fifth root of 40 (5√40) = 2.09128 Fifth root of 41 (5√41) = 2.10163 Fifth root of 42 (5√42) = 2.11179 Fifth root of 43 (5√43) = 2.12175 Fifth root of 44 (5√44) = 2.13153 Fifth root of 45 (5√45) = 2.14113 Fifth root of 46 (5√46) = 2.15056 Fifth root of 47 (5√47) = 2.15983 Fifth root of 48 (5√48) = 2.16894 Fifth root of 49 (5√49) = 2.17791 Fifth root of 50 (5√50) = 2.18672 Fifth root of 51 (5√51) = 2.1954 Fifth root of 52 (5√52) = 2.20394 Fifth root of 53 (5√53) = 2.21236 Fifth root of 54 (5√54) = 2.22064 Fifth root of 55 (5√55) = 2.22881 Fifth root of 56 (5√56) = 2.23685 Fifth root of 57 (5√57) = 2.24479 Fifth root of 58 (5√58) = 2.25261 Fifth root of 59 (5√59) = 2.26032 Fifth root of 60 (5√60) = 2.26793 Fifth root of 61 (5√61) = 2.27544 Fifth root of 62 (5√62) = 2.28286 Fifth root of 63 (5√63) = 2.29017 Fifth root of 64 (5√64) = 2.2974 Fifth root of 65 (5√65) = 2.30453 Fifth root of 66 (5√66) = 2.31158 Fifth root of 67 (5√67) = 2.31854 Fifth root of 68 (5√68) = 2.32542 Fifth root of 69 (5√69) = 2.33222 Fifth root of 70 (5√70) = 2.33894 Fifth root of 71 (5√71) = 2.34559 Fifth root of 72 (5√72) = 2.35216 Fifth root of 73 (5√73) = 2.35866 Fifth root of 74 (5√74) = 2.36508 Fifth root of 75 (5√75) = 2.37144 Fifth root of 76 (5√76) = 2.37773 Fifth root of 77 (5√77) = 2.38396 Fifth root of 78 (5√78) = 2.39012 Fifth root of 79 (5√79) = 2.39621 Fifth root of 80 (5√80) = 2.40225 Fifth root of 81 (5√81) = 2.40822 Fifth root of 82 (5√82) = 2.41414 Fifth root of 83 (5√83) = 2.42 Fifth root of 84 (5√84) = 2.4258 Fifth root of 85 (5√85) = 2.43155 Fifth root of 86 (5√86) = 2.43725 Fifth root of 87 (5√87) = 2.44289 Fifth root of 88 (5√88) = 2.44848 Fifth root of 89 (5√89) = 2.45402 Fifth root of 90 (5√90) = 2.45951 Fifth root of 91 (5√91) = 2.46495 Fifth root of 92 (5√92) = 2.47034 Fifth root of 93 (5√93) = 2.47569 Fifth root of 94 (5√94) = 2.48099 Fifth root of 95 (5√95) = 2.48625 Fifth root of 96 (5√96) = 2.49146 Fifth root of 97 (5√97) = 2.49663 Fifth root of 98 (5√98) = 2.50176 Fifth root of 99 (5√99) = 2.50684 Fifth root of 100 (5√100) = 2.51189