### 6th Root Calculator

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### What is a sixth root?

The sixth root of a number is the number that would have to be multiplied by itself 6 times to get the original number.

For example, the sixth root of 729 is 3 as 3 x 3 x 3 x 3 x 3 x 3 is 729.

The sixth root of 4,096 is 4, as 4 x 4 x 4 x 4 x 4 x 4 is 4,096.

For example, the sixth root of 729 is 3 as 3 x 3 x 3 x 3 x 3 x 3 is 729.

The sixth root of 4,096 is 4, as 4 x 4 x 4 x 4 x 4 x 4 is 4,096.

### How to calculate sixth root

Even for perfect sixth root numbers, sixth root can be difficult to calculate by hand.

The most basic techniques involve trial and error.

Example:

Find the sixth root of 262,144

1) Try a number – 5 : 5 x 5 x 5 x 5 x 5 x 5 = 163,840 (too low)

2) Try another number that is more than 5 – 6 : 6 x 6 x 6 x 6 x 6 x 6 = 46,656(too low)

3) Try a number that is more than 6 – 10 – 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000 (too high)

4) Try a number in between 6 and 10 – 8 – 8 x 8 x 8 x 8 x 8 x 8 = 262,144 (answer)

A sixth root can also be calculated as the same number to the exponent 1/6.

The most basic techniques involve trial and error.

Example:

Find the sixth root of 262,144

1) Try a number – 5 : 5 x 5 x 5 x 5 x 5 x 5 = 163,840 (too low)

2) Try another number that is more than 5 – 6 : 6 x 6 x 6 x 6 x 6 x 6 = 46,656(too low)

3) Try a number that is more than 6 – 10 – 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000 (too high)

4) Try a number in between 6 and 10 – 8 – 8 x 8 x 8 x 8 x 8 x 8 = 262,144 (answer)

A sixth root can also be calculated as the same number to the exponent 1/6.

^{6}√number = number^{1/6}### Table – Sixth Root (^{6}√) of 1 – 100

Sixth root of 0 (^{6}√0) |
= | 0.00000000000000000000 |

Sixth root of 1 (^{6}√1) |
= | 1.00000000000000000000 |

Sixth root of 2 (^{6}√2) |
= | 1.12246204830937301722 |

Sixth root of 3 (^{6}√3) |
= | 1.20093695517600274059 |

Sixth root of 4 (^{6}√4) |
= | 1.25992104989487319067 |

Sixth root of 5 (^{6}√5) |
= | 1.30766048601183060285 |

Sixth root of 6 (^{6}√6) |
= | 1.34800615459727768375 |

Sixth root of 7 (^{6}√7) |
= | 1.38308755426848839498 |

Sixth root of 8 (^{6}√8) |
= | 1.41421356237309492343 |

Sixth root of 9 (^{6}√9) |
= | 1.44224957030740830177 |

Sixth root of 10 (^{6}√10) |
= | 1.46779926762206947011 |

Sixth root of 11 (^{6}√11) |
= | 1.49130147541310886794 |

Sixth root of 12 (^{6}√12) |
= | 1.51308574942290152698 |

Sixth root of 13 (^{6}√13) |
= | 1.53340623701638745224 |

Sixth root of 14 (^{6}√14) |
= | 1.55246328915540865445 |

Sixth root of 15 (^{6}√15) |
= | 1.57041780247501971957 |

Sixth root of 16 (^{6}√16) |
= | 1.58740105196819936140 |

Sixth root of 17 (^{6}√17) |
= | 1.60352162151254917788 |

Sixth root of 18 (^{6}√18) |
= | 1.61887040686056660199 |

Sixth root of 19 (^{6}√19) |
= | 1.63352430307049445446 |

Sixth root of 20 (^{6}√20) |
= | 1.64754897244206555129 |

Sixth root of 21 (^{6}√21) |
= | 1.66100095616502296814 |

Sixth root of 22 (^{6}√22) |
= | 1.67392930873898815314 |

Sixth root of 23 (^{6}√23) |
= | 1.68637687954133341783 |

Sixth root of 24 (^{6}√24) |
= | 1.69838132956495280190 |

Sixth root of 25 (^{6}√25) |
= | 1.70997594667669683410 |

Sixth root of 26 (^{6}√26) |
= | 1.72119030569178210754 |

Sixth root of 27 (^{6}√27) |
= | 1.73205080756887719318 |

Sixth root of 28 (^{6}√28) |
= | 1.74258112347048643720 |

Sixth root of 29 (^{6}√29) |
= | 1.75280256323575911459 |

Sixth root of 30 (^{6}√30) |
= | 1.76273438326761500150 |

Sixth root of 31 (^{6}√31) |
= | 1.77239404546263146223 |

Sixth root of 32 (^{6}√32) |
= | 1.78179743628067854821 |

Sixth root of 33 (^{6}√33) |
= | 1.79095905313209957654 |

Sixth root of 34 (^{6}√34) |
= | 1.79989216379134320256 |

Sixth root of 35 (^{6}√35) |
= | 1.80860894341164568644 |

Sixth root of 36 (^{6}√36) |
= | 1.81712059283213966943 |

Sixth root of 37 (^{6}√37) |
= | 1.82543744117566331120 |

Sixth root of 38 (^{6}√38) |
= | 1.83356903518764813299 |

Sixth root of 39 (^{6}√39) |
= | 1.84152421733035231988 |

Sixth root of 40 (^{6}√40) |
= | 1.84931119429732371273 |

Sixth root of 41 (^{6}√41) |
= | 1.85693759733135088652 |

Sixth root of 42 (^{6}√42) |
= | 1.86441053550081869972 |

Sixth root of 43 (^{6}√43) |
= | 1.87173664290324870407 |

Sixth root of 44 (^{6}√44) |
= | 1.87892212061225749586 |

Sixth root of 45 (^{6}√45) |
= | 1.88597277405853946952 |

Sixth root of 46 (^{6}√46) |
= | 1.89289404643153402752 |

Sixth root of 47 (^{6}√47) |
= | 1.89969104860203374940 |

Sixth root of 48 (^{6}√48) |
= | 1.90636858599387304380 |

Sixth root of 49 (^{6}√49) |
= | 1.91293118277238893832 |

Sixth root of 50 (^{6}√50) |
= | 1.91938310366648434702 |

Sixth root of 51 (^{6}√51) |
= | 1.92572837369816762809 |

Sixth root of 52 (^{6}√52) |
= | 1.93197079605703359029 |

Sixth root of 53 (^{6}√53) |
= | 1.93811396832618476616 |

Sixth root of 54 (^{6}√54) |
= | 1.94416129723966557563 |

Sixth root of 55 (^{6}√55) |
= | 1.95011601212886587220 |

Sixth root of 56 (^{6}√56) |
= | 1.95598117719593056485 |

Sixth root of 57 (^{6}√57) |
= | 1.96175970273548161416 |

Sixth root of 58 (^{6}√58) |
= | 1.96745435541152935421 |

Sixth root of 59 (^{6}√59) |
= | 1.97306776768393343779 |

Sixth root of 60 (^{6}√60) |
= | 1.97860244646792637901 |

Sixth root of 61 (^{6}√61) |
= | 1.98406078110076378174 |

Sixth root of 62 (^{6}√62) |
= | 1.98944505068132126979 |

Sixth root of 63 (^{6}√63) |
= | 1.99475743084125189952 |

Sixth root of 64 (^{6}√64) |
= | 2.00000000000000000000 |

Sixth root of 65 (^{6}√65) |
= | 2.00517474515042160021 |

Sixth root of 66 (^{6}√66) |
= | 2.01028356721687151420 |

Sixth root of 67 (^{6}√67) |
= | 2.01532828602331681722 |

Sixth root of 68 (^{6}√68) |
= | 2.02031064490522060950 |

Sixth root of 69 (^{6}√69) |
= | 2.02523231499557798685 |

Sixth root of 70 (^{6}√70) |
= | 2.03009489921248675870 |

Sixth root of 71 (^{6}√71) |
= | 2.03489993597298379768 |

Sixth root of 72 (^{6}√72) |
= | 2.03964890265550558013 |

Sixth root of 73 (^{6}√73) |
= | 2.04434321883122915864 |

Sixth root of 74 (^{6}√74) |
= | 2.04898424928265532330 |

Sixth root of 75 (^{6}√75) |
= | 2.05357330682611527450 |

Sixth root of 76 (^{6}√76) |
= | 2.05811165495336823028 |

Sixth root of 77 (^{6}√77) |
= | 2.06260051030610513934 |

Sixth root of 78 (^{6}√78) |
= | 2.06704104499594221167 |

Sixth root of 79 (^{6}√79) |
= | 2.07143438878140839776 |

Sixth root of 80 (^{6}√80) |
= | 2.07578163111242686156 |

Sixth root of 81 (^{6}√81) |
= | 2.08008382305190409056 |

Sixth root of 82 (^{6}√82) |
= | 2.08434197908323382009 |

Sixth root of 83 (^{6}√83) |
= | 2.08855707881178975782 |

Sixth root of 84 (^{6}√84) |
= | 2.09273006856782384233 |

Sixth root of 85 (^{6}√85) |
= | 2.09686186291757881150 |

Sixth root of 86 (^{6}√86) |
= | 2.10095334608889006134 |

Sixth root of 87 (^{6}√87) |
= | 2.10500537331704551391 |

Sixth root of 88 (^{6}√88) |
= | 2.10901877211622545971 |

Sixth root of 89 (^{6}√89) |
= | 2.11299434348143444495 |

Sixth root of 90 (^{6}√90) |
= | 2.11693286302545846667 |

Sixth root of 91 (^{6}√91) |
= | 2.12083508205504145394 |

Sixth root of 92 (^{6}√92) |
= | 2.12470172859015704603 |

Sixth root of 93 (^{6}√93) |
= | 2.12853350832997056941 |

Sixth root of 94 (^{6}√94) |
= | 2.13233110556881921838 |

Sixth root of 95 (^{6}√95) |
= | 2.13609518406529952372 |

Sixth root of 96 (^{6}√96) |
= | 2.13982638786732559666 |

Sixth root of 97 (^{6}√97) |
= | 2.14352534209582890057 |

Sixth root of 98 (^{6}√98) |
= | 2.14719265368956735429 |

Sixth root of 99 (^{6}√99) |
= | 2.15082891211336058035 |

Sixth root of 100 (^{6}√100) |
= | 2.15443469003188381450 |