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Fifth Root

5th Root Calculator

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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) = 0.00000000000000000000
Fifth root of 1 (5√1) = 1.00000000000000000000
Fifth root of 2 (5√2) = 1.14869835499703509818
Fifth root of 3 (5√3) = 1.24573093961551739639
Fifth root of 4 (5√4) = 1.31950791077289419917
Fifth root of 5 (5√5) = 1.37972966146121489572
Fifth root of 6 (5√6) = 1.43096908110525555813
Fifth root of 7 (5√7) = 1.47577316159455218525
Fifth root of 8 (5√8) = 1.51571656651039821107
Fifth root of 9 (5√9) = 1.55184557391535959958
Fifth root of 10 (5√10) = 1.58489319246111359796
Fifth root of 11 (5√11) = 1.61539426620217807518
Fifth root of 12 (5√12) = 1.64375182951722575986
Fifth root of 13 (5√13) = 1.67027765233481040319
Fifth root of 14 (5√14) = 1.69521820307243542558
Fifth root of 15 (5√15) = 1.71877192758747887602
Fifth root of 16 (5√16) = 1.74110112659224824938
Fifth root of 17 (5√17) = 1.76234034783231696686
Fifth root of 18 (5√18) = 1.78260245796600336199
Fifth root of 19 (5√19) = 1.80198312731714227475
Fifth root of 20 (5√20) = 1.82056420302608046313
Fifth root of 21 (5√21) = 1.83841628725254402354
Fifth root of 22 (5√22) = 1.85560073625808441555
Fifth root of 23 (5√23) = 1.87217123055485745731
Fifth root of 24 (5√24) = 1.88817502258980396412
Fifth root of 25 (5√25) = 1.90365393871587862407
Fifth root of 26 (5√26) = 1.91864519162530622332
Fifth root of 27 (5√27) = 1.93318204493176293290
Fifth root of 28 (5√28) = 1.94729436123033639028
Fifth root of 29 (5√29) = 1.96100905745454823226
Fifth root of 30 (5√30) = 1.97435048583481997930
Fifth root of 31 (5√31) = 1.98734075466445792024
Fifth root of 32 (5√32) = 2.00000000000000000000
Fifth root of 33 (5√33) = 2.01234661708555861992
Fifth root of 34 (5√34) = 2.02439745849988517179
Fifth root of 35 (5√35) = 2.03616800464039826579
Fifth root of 36 (5√36) = 2.04767251107921932629
Fifth root of 37 (5√37) = 2.05892413647851713066
Fifth root of 38 (5√38) = 2.06993505408161393433
Fifth root of 39 (5√39) = 2.08071654926184379519
Fifth root of 40 (5√40) = 2.09127910518254633843
Fifth root of 41 (5√41) = 2.10163247827578469895
Fifth root of 42 (5√42) = 2.11178576496675418639
Fifth root of 43 (5√43) = 2.12174746084189802531
Fifth root of 44 (5√44) = 2.13152551327094830214
Fifth root of 45 (5√45) = 2.14112736833832384420
Fifth root of 46 (5√46) = 2.15056001281113973178
Fifth root of 47 (5√47) = 2.15983001176446620661
Fifth root of 48 (5√48) = 2.16894354239539755014
Fifth root of 49 (5√49) = 2.17790642448278015664
Fifth root of 50 (5√50) = 2.18672414788655622431
Fifth root of 51 (5√51) = 2.19540189742749003443
Fifth root of 52 (5√52) = 2.20394457544296029639
Fifth root of 53 (5√53) = 2.21235682227611674122
Fifth root of 54 (5√54) = 2.22064303492292047792
Fifth root of 55 (5√55) = 2.22880738403351852384
Fifth root of 56 (5√56) = 2.23685382944028976482
Fifth root of 57 (5√57) = 2.24478613436409224491
Fifth root of 58 (5√58) = 2.25260787843232579419
Fifth root of 59 (5√59) = 2.26032246962681604430
Fifth root of 60 (5√60) = 2.26793315526605487875
Fifth root of 61 (5√61) = 2.27544303211453069480
Fifth root of 62 (5√62) = 2.28285505570162916555
Fifth root of 63 (5√63) = 2.29017204892358261503
Fifth root of 64 (5√64) = 2.29739670999407019636
Fifth root of 65 (5√65) = 2.30453161980214105142
Fifth root of 66 (5√66) = 2.31157924873002906807
Fifth root of 67 (5√67) = 2.31854196297805037474
Fifth root of 68 (5√68) = 2.32542203043899631254
Fifth root of 69 (5√69) = 2.33222162616024197845
Fifth root of 70 (5√70) = 2.33894283742802011616
Fifth root of 71 (5√71) = 2.34558766850500299839
Fifth root of 72 (5√72) = 2.35215804504934711261
Fifth root of 73 (5√73) = 2.35865581824073577977
Fifth root of 74 (5√74) = 2.36508276863656341504
Fifth root of 75 (5√75) = 2.37144060977931170342
Fifth root of 76 (5√76) = 2.37773099157424905314
Fifth root of 77 (5√77) = 2.38395550345489981581
Fifth root of 78 (5√78) = 2.39011567735218699582
Fifth root of 79 (5√79) = 2.39621299048177016644
Fifth root of 80 (5√80) = 2.40224886796286263291
Fifth root of 81 (5√81) = 2.40822468528069233429
Fifth root of 82 (5√82) = 2.41414177060373624784
Fifth root of 83 (5√83) = 2.42000140696596233170
Fifth root of 84 (5√84) = 2.42580483432346527550
Fifth root of 85 (5√85) = 2.43155325149412249175
Fifth root of 86 (5√86) = 2.43724781798822398571
Fifth root of 87 (5√87) = 2.44288965573739424997
Fifth root of 88 (5√88) = 2.44847985072854967825
Fifth root of 89 (5√89) = 2.45401945454913050781
Fifth root of 90 (5√90) = 2.45950948584936313068
Fifth root of 91 (5√91) = 2.46495093172686940974
Fifth root of 92 (5√92) = 2.47034474903855860717
Fifth root of 93 (5√93) = 2.47569186564436627407
Fifth root of 94 (5√94) = 2.48099318158706916293
Fifth root of 95 (5√95) = 2.48624957021210191144
Fifth root of 96 (5√96) = 2.49146187923103479278
Fifth root of 97 (5√97) = 2.49663093173208716635
Fifth root of 98 (5√98) = 2.50175752714084342898
Fifth root of 99 (5√99) = 2.50684244213410023505
Fifth root of 100 (5√100) = 2.51188643150958013095

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