Fourth Root

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What is a fourth root?

The fourth root of a number is the number that would have to be multiplied by itself 4 times to get the original number.
For example, the fourth root of 81 is 3 as 3 x 3 x 3 x 3 is 81.
The fourth root of 104,976 is 18, as 18 x 18 x 18 x 18 is 104,976.

How to calculate fourth root

Even for perfect fourth root numbers, fourth root can be difficult to calculate by hand.
The most basic techniques involve trial and error.
Example:
Find the fourth root of 4,096
1) Try a number – 5 : 5 x 5 x 5 x 5 = 625 (too low)
2) Try another number that is more than 5 – 6 : 6 x 6 x 6 x 6 = 1,296 (too low)
3) Try a number that is more than 6 – 10 – 10 x 10 x 10 x 10 = 10,000 (too high)
4) Try a number in between 6 and 10 – 8 – 8 x 8 x 8 x 8 = 4,096 (answer)
A fourth root can also be calculated as the same number to the exponent 1/4.
4√number = number1/4

Table – Fourth Root (4√) of 1 – 100

 Fourth root of 0 (4√0) = 0 Fourth root of 1 (4√1) = 1 Fourth root of 2 (4√2) = 1.18921 Fourth root of 3 (4√3) = 1.31607 Fourth root of 4 (4√4) = 1.41421 Fourth root of 5 (4√5) = 1.49535 Fourth root of 6 (4√6) = 1.56508 Fourth root of 7 (4√7) = 1.62658 Fourth root of 8 (4√8) = 1.68179 Fourth root of 9 (4√9) = 1.73205 Fourth root of 10 (4√10) = 1.77828 Fourth root of 11 (4√11) = 1.82116 Fourth root of 12 (4√12) = 1.86121 Fourth root of 13 (4√13) = 1.89883 Fourth root of 14 (4√14) = 1.93434 Fourth root of 15 (4√15) = 1.96799 Fourth root of 16 (4√16) = 2 Fourth root of 17 (4√17) = 2.03054 Fourth root of 18 (4√18) = 2.05977 Fourth root of 19 (4√19) = 2.0878 Fourth root of 20 (4√20) = 2.11474 Fourth root of 21 (4√21) = 2.1407 Fourth root of 22 (4√22) = 2.16574 Fourth root of 23 (4√23) = 2.18994 Fourth root of 24 (4√24) = 2.21336 Fourth root of 25 (4√25) = 2.23607 Fourth root of 26 (4√26) = 2.2581 Fourth root of 27 (4√27) = 2.27951 Fourth root of 28 (4√28) = 2.30033 Fourth root of 29 (4√29) = 2.3206 Fourth root of 30 (4√30) = 2.34035 Fourth root of 31 (4√31) = 2.35961 Fourth root of 32 (4√32) = 2.37841 Fourth root of 33 (4√33) = 2.39678 Fourth root of 34 (4√34) = 2.41474 Fourth root of 35 (4√35) = 2.4323 Fourth root of 36 (4√36) = 2.44949 Fourth root of 37 (4√37) = 2.46633 Fourth root of 38 (4√38) = 2.48282 Fourth root of 39 (4√39) = 2.499 Fourth root of 40 (4√40) = 2.51487 Fourth root of 41 (4√41) = 2.53044 Fourth root of 42 (4√42) = 2.54573 Fourth root of 43 (4√43) = 2.56075 Fourth root of 44 (4√44) = 2.57551 Fourth root of 45 (4√45) = 2.59002 Fourth root of 46 (4√46) = 2.60429 Fourth root of 47 (4√47) = 2.61833 Fourth root of 48 (4√48) = 2.63215 Fourth root of 49 (4√49) = 2.64575 Fourth root of 50 (4√50) = 2.65915 Fourth root of 51 (4√51) = 2.67235 Fourth root of 52 (4√52) = 2.68535 Fourth root of 53 (4√53) = 2.69817 Fourth root of 54 (4√54) = 2.71081 Fourth root of 55 (4√55) = 2.72327 Fourth root of 56 (4√56) = 2.73556 Fourth root of 57 (4√57) = 2.7477 Fourth root of 58 (4√58) = 2.75967 Fourth root of 59 (4√59) = 2.77149 Fourth root of 60 (4√60) = 2.78316 Fourth root of 61 (4√61) = 2.79468 Fourth root of 62 (4√62) = 2.80607 Fourth root of 63 (4√63) = 2.81731 Fourth root of 64 (4√64) = 2.82843 Fourth root of 65 (4√65) = 2.83941 Fourth root of 66 (4√66) = 2.85027 Fourth root of 67 (4√67) = 2.86101 Fourth root of 68 (4√68) = 2.87162 Fourth root of 69 (4√69) = 2.88212 Fourth root of 70 (4√70) = 2.89251 Fourth root of 71 (4√71) = 2.90278 Fourth root of 72 (4√72) = 2.91295 Fourth root of 73 (4√73) = 2.92301 Fourth root of 74 (4√74) = 2.93297 Fourth root of 75 (4√75) = 2.94283 Fourth root of 76 (4√76) = 2.95259 Fourth root of 77 (4√77) = 2.96226 Fourth root of 78 (4√78) = 2.97183 Fourth root of 79 (4√79) = 2.98131 Fourth root of 80 (4√80) = 2.9907 Fourth root of 81 (4√81) = 3 Fourth root of 82 (4√82) = 3.00922 Fourth root of 83 (4√83) = 3.01835 Fourth root of 84 (4√84) = 3.0274 Fourth root of 85 (4√85) = 3.03637 Fourth root of 86 (4√86) = 3.04526 Fourth root of 87 (4√87) = 3.05408 Fourth root of 88 (4√88) = 3.06281 Fourth root of 89 (4√89) = 3.07148 Fourth root of 90 (4√90) = 3.08007 Fourth root of 91 (4√91) = 3.08859 Fourth root of 92 (4√92) = 3.09704 Fourth root of 93 (4√93) = 3.10542 Fourth root of 94 (4√94) = 3.11374 Fourth root of 95 (4√95) = 3.12199 Fourth root of 96 (4√96) = 3.13017 Fourth root of 97 (4√97) = 3.13829 Fourth root of 98 (4√98) = 3.14635 Fourth root of 99 (4√99) = 3.15434 Fourth root of 100 (4√100) = 3.16228