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Eighth Root Calculator

8th Root Calculator

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What is an eighth root?

The eighth root of a number is the number that would have to be multiplied by itself 8 times to get the original number.
For example, the eighth root of 6,561 is 3 as 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 is 6,561.
The eighth root of 57,536 is 4, as 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 is 57,536.

How to calculate eighth root

Even for perfect eighth root numbers, eighth root can be difficult to calculate by hand.
The most basic techniques involve trial and error.
Example:
Find the eighth root of 16,777,216
1) Try a number – 5 : 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 390,625 (too low)
2) Try another number that is more than 5 – 6 : 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 = 1,679,616 (too low)
3) Try a number that is more than 6 – 10 – 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 100,000,000 (too high)
4) Try a number in between 6 and 10 – 8 – 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 = 16,777,216 (answer)
An eighth root can also be calculated as the same number to the exponent 1/8.
8√number = number1/8

Table – Eighth Root (8√) of 1 – 100

Eighth root of 0 (8√0) = 0.00000000000000000000
Eighth root of 1 (8√1) = 1.00000000000000000000
Eighth root of 2 (8√2) = 1.09050773266525768967
Eighth root of 3 (8√3) = 1.14720269043987710411
Eighth root of 4 (8√4) = 1.18920711500272102690
Eighth root of 5 (8√5) = 1.22284454499385186743
Eighth root of 6 (8√6) = 1.25103340485907388313
Eighth root of 7 (8√7) = 1.27537310685845417524
Eighth root of 8 (8√8) = 1.29683955465100964055
Eighth root of 9 (8√9) = 1.31607401295249237805
Eighth root of 10 (8√10) = 1.33352143216332397202
Eighth root of 11 (8√11) = 1.34950371871954177827
Eighth root of 12 (8√12) = 1.36426160182136602117
Eighth root of 13 (8√13) = 1.37798001513662815576
Eighth root of 14 (8√14) = 1.39080423506245809406
Eighth root of 15 (8√15) = 1.40285055200667407860
Eighth root of 16 (8√16) = 1.41421356237309514547
Eighth root of 17 (8√17) = 1.42497129264730482134
Eighth root of 18 (8√18) = 1.43518888788448939486
Eighth root of 19 (8√19) = 1.44492132309335241658
Eighth root of 20 (8√20) = 1.45421543344895365379
Eighth root of 21 (8√21) = 1.46311145950268350902
Eighth root of 22 (8√22) = 1.47164424052418096878
Eighth root of 23 (8√23) = 1.47984414824495691398
Eighth root of 24 (8√24) = 1.48773782616449024019
Eighth root of 25 (8√25) = 1.49534878122122050215
Eighth root of 26 (8√26) = 1.50269786196468158046
Eighth root of 27 (8√27) = 1.50980364847710490928
Eighth root of 28 (8√28) = 1.51668277295919917691
Eighth root of 29 (8√29) = 1.52335018531724464275
Eighth root of 30 (8√30) = 1.52981937473700346786
Eighth root of 31 (8√31) = 1.53610255574638210341
Eighth root of 32 (8√32) = 1.54221082540794074411
Eighth root of 33 (8√33) = 1.54815429687367744904
Eighth root of 34 (8√34) = 1.55394221345789373956
Eighth root of 35 (8√35) = 1.55958304655372148595
Eighth root of 36 (8√36) = 1.56508458007328732364
Eighth root of 37 (8√37) = 1.57045398358553023321
Eighth root of 38 (8√38) = 1.57569787592621590733
Eighth root of 39 (8√39) = 1.58082238073712244564
Eighth root of 40 (8√40) = 1.58583317513724342263
Eighth root of 41 (8√41) = 1.59073553252426047599
Eighth root of 42 (8√42) = 1.59553436033882722889
Eighth root of 43 (8√43) = 1.60023423348927718024
Eighth root of 44 (8√44) = 1.60483942402390966642
Eighth root of 45 (8√45) = 1.60935392754712336405
Eighth root of 46 (8√46) = 1.61378148680055755193
Eighth root of 47 (8√47) = 1.61812561276802169274
Eighth root of 48 (8√48) = 1.62238960361097750429
Eighth root of 49 (8√49) = 1.62657656169778586097
Eighth root of 50 (8√50) = 1.63068940895330949381
Eighth root of 51 (8√51) = 1.63473090072457738486
Eighth root of 52 (8√52) = 1.63870363833203525061
Eighth root of 53 (8√53) = 1.64261008045369227837
Eighth root of 54 (8√54) = 1.64645255347050145645
Eighth root of 55 (8√55) = 1.65023326088510913223
Eighth root of 56 (8√56) = 1.65395429191219212051
Eighth root of 57 (8√57) = 1.65761762932664069581
Eighth root of 58 (8√58) = 1.66122515664550851611
Eighth root of 59 (8√59) = 1.66477866471072855070
Eighth root of 60 (8√60) = 1.66827985773183162799
Eighth root of 61 (8√61) = 1.67173035884117426875
Eighth root of 62 (8√62) = 1.67513171520829473593
Eighth root of 63 (8√63) = 1.67848540275489366280
Eighth root of 64 (8√64) = 1.68179283050742900407
Eighth root of 65 (8√65) = 1.68505534462037109833
Eighth root of 66 (8√66) = 1.68827423209968996431
Eighth root of 67 (8√67) = 1.69145072425309073161
Eighth root of 68 (8√68) = 1.69458599989079949921
Eighth root of 69 (8√69) = 1.69768118829832292960
Eighth root of 70 (8√70) = 1.70073737200047370166
Eighth root of 71 (8√71) = 1.70375558933407456053
Eighth root of 72 (8√72) = 1.70673683684507748737
Eighth root of 73 (8√73) = 1.70968207152434192864
Eighth root of 74 (8√74) = 1.71259221289497820528
Eighth root of 75 (8√75) = 1.71546814496297539421
Eighth root of 76 (8√76) = 1.71831071804176005458
Eighth root of 77 (8√77) = 1.72112075046037915627
Eighth root of 78 (8√78) = 1.72389903016413392756
Eighth root of 79 (8√79) = 1.72664631621572439713
Eighth root of 80 (8√80) = 1.72936334020426185631
Eighth root of 81 (8√81) = 1.73205080756887719318
Eighth root of 82 (8√82) = 1.73470939884309260925
Eighth root of 83 (8√83) = 1.73733977082559554184
Eighth root of 84 (8√84) = 1.73994255768260663864
Eighth root of 85 (8√85) = 1.74251837198659420558
Eighth root of 86 (8√86) = 1.74506780569571828821
Eighth root of 87 (8√87) = 1.74759143107802827899
Eighth root of 88 (8√88) = 1.75008980158413196548
Eighth root of 89 (8√89) = 1.75256345267175217550
Eighth root of 90 (8√90) = 1.75501290258534070610
Eighth root of 91 (8√91) = 1.75743865309366098515
Eighth root of 92 (8√92) = 1.75984119018804441303
Eighth root of 93 (8√93) = 1.76222098474382082856
Eighth root of 94 (8√94) = 1.76457849314723591583
Eighth root of 95 (8√95) = 1.76691415789000494385
Eighth root of 96 (8√96) = 1.76922840813349324662
Eighth root of 97 (8√97) = 1.77152166024437773828
Eighth root of 98 (8√98) = 1.77379431830350298149
Eighth root of 99 (8√99) = 1.77604677458953874591
Eighth root of 100 (8√100) = 1.77827941003892275873

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