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Eighth Root Calculator

8th Root Calculator

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)=1.46311145950268328697
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)=1.50269786196468180250
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)=1.57045398358553001117
Eighth root of 38 (8√38)=1.57569787592621590733
Eighth root of 39 (8√39)=1.58082238073712222359
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)=1.62657656169778563893
Eighth root of 50 (8√50)=1.63068940895330971586
Eighth root of 51 (8√51)=1.63473090072457738486
Eighth root of 52 (8√52)=1.63870363833203547266
Eighth root of 53 (8√53)=1.64261008045369227837
Eighth root of 54 (8√54)=1.64645255347050145645
Eighth root of 55 (8√55)=1.65023326088510891019
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)=1.68827423209969018636
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)=1.72936334020426163427
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)=1.74759143107802850103
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)=1.77152166024437751624
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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