Table of Contents

In math, the **5th root** *b* of a number *a* is such that b^{5} = a. By definition, when you multiply b by itself *5* times you get the value of a.

A 5-th root is usually denoted ^{5}√x, but it can also be written in exponential form with the base *x* and the exponent 1/5: x^1/5 or x^{1/5}.

Read on to learn everything about these numbers, including the properties, and make sure to check out our calculator.

## Calculator

If you happen to know exponentiation, then you can think of the 5th root of a number as the inverse operation to elevating a number to the power of 5.

## Definition

Whereas in exponentiation elevating a number *a* to the power of 5 is defined as a^{5} = b, the 5th root *b* is defined as b = a^{1/5}.

For example with a = 7776 we get:

In other words, the 5th root of 7776 is 6, because 6 times 6 times 6 times 6 times 6 is 7776.

As the index n (5) is odd, 5 is the only real 5th root.

You may be interested what happens if the nth Root index *n* of a root is is even.

Keep reading to learn everything about the fifth root.

On this Site You Can Find all About 5th Roots, Including a Calculator! Click To Tweet

Next, we explain how the parts are called. Keep reading to learn all about the topic.

## Parts

As depicted, the parts of the fifth root are:

The radix sign, which tells us that it is a mathematical root, and the index of *5*, which tells us that it is the 5-th root.

The number below the radix, x, is the radicand.

The result of the mathematical operation is denoted by the equal sign and called the root.

### 5th Root Symbol

The symbol √ is called radical sign, or radix.

Ahead is our calculator.

## About our 5th Root Calculator

Our calculator at the top of this page computes the fifth root of any non-negative real number.

Just enter a valid radicand; you then automatically obtain the result.

If this app has been of use to you bookmark it now.

Next, we discuss the properties.

## 5th Root Properties

With

= -a if a < 0 and a if ≥ 0

The most important property is the first; the negative number tends to be forgotten. Read on to see the examples:

## 5th Root Examples

We use the list of properties above to show you some examples in the order of appearance:

Frequently searched terms on this site include:

## 5th Root in Excel

In Excel you enter the syntax for

in a cell, like this:

=POWER(radicand,1/5)

For example, to calculate

insert =POWER(60,1/6).

In the next section we explain how to do the math.

## How to Calculate the 5th Root

A very efficient procedure for extracting the fifth root is the Newton–Raphson method, also known as Newton’s method detailed below:

You begin with a guessed starting value and then iterate the steps until you’re happy with the precision.

In the most basic version of the method, f is a single-variable function and f′ its derivative.

You may think of it as the 5th root formula.

Next are frequently asked questions in the context of this article.

## FAQs

Click on the question which is of interest to you to see the collapsible content answer.

### What is the 5th Root Called?

### How Do You Type a 5th Root on a Computer?

### How Do You do 5th Roots on a Calculator?

## Table of Fifth Roots

Radicand | Symbol | 5th Root |
---|---|---|

0 | ⁵√0 | 0 |

1 | ⁵√1 | 1 |

2 | ⁵√2 | 1.148698355 |

3 | ⁵√3 | 1.2457309396 |

4 | ⁵√4 | 1.3195079108 |

5 | ⁵√5 | 1.3797296615 |

6 | ⁵√6 | 1.4309690811 |

7 | ⁵√7 | 1.4757731616 |

8 | ⁵√8 | 1.5157165665 |

9 | ⁵√9 | 1.5518455739 |

10 | ⁵√10 | 1.5848931925 |

11 | ⁵√11 | 1.6153942662 |

12 | ⁵√12 | 1.6437518295 |

13 | ⁵√13 | 1.6702776523 |

14 | ⁵√14 | 1.6952182031 |

15 | ⁵√15 | 1.7187719276 |

16 | ⁵√16 | 1.7411011266 |

17 | ⁵√17 | 1.7623403478 |

18 | ⁵√18 | 1.782602458 |

19 | ⁵√19 | 1.8019831273 |

20 | ⁵√20 | 1.820564203 |

21 | ⁵√21 | 1.8384162873 |

22 | ⁵√22 | 1.8556007363 |

23 | ⁵√23 | 1.8721712306 |

24 | ⁵√24 | 1.8881750226 |

25 | ⁵√25 | 1.9036539387 |

26 | ⁵√26 | 1.9186451916 |

27 | ⁵√27 | 1.9331820449 |

28 | ⁵√28 | 1.9472943612 |

29 | ⁵√29 | 1.9610090575 |

30 | ⁵√30 | 1.9743504858 |

31 | ⁵√31 | 1.9873407547 |

32 | ⁵√32 | 2 |

33 | ⁵√33 | 2.0123466171 |

34 | ⁵√34 | 2.0243974585 |

35 | ⁵√35 | 2.0361680046 |

36 | ⁵√36 | 2.0476725111 |

37 | ⁵√37 | 2.0589241365 |

38 | ⁵√38 | 2.0699350541 |

39 | ⁵√39 | 2.0807165493 |

40 | ⁵√40 | 2.0912791052 |

41 | ⁵√41 | 2.1016324783 |

42 | ⁵√42 | 2.111785765 |

43 | ⁵√43 | 2.1217474608 |

44 | ⁵√44 | 2.1315255133 |

45 | ⁵√45 | 2.1411273683 |

46 | ⁵√46 | 2.1505600128 |

47 | ⁵√47 | 2.1598300118 |

48 | ⁵√48 | 2.1689435424 |

49 | ⁵√49 | 2.1779064245 |

50 | ⁵√50 | 2.1867241479 |

51 | ⁵√51 | 2.1954018974 |

52 | ⁵√52 | 2.2039445754 |

53 | ⁵√53 | 2.2123568223 |

54 | ⁵√54 | 2.2206430349 |

55 | ⁵√55 | 2.228807384 |

56 | ⁵√56 | 2.2368538294 |

57 | ⁵√57 | 2.2447861344 |

58 | ⁵√58 | 2.2526078784 |

59 | ⁵√59 | 2.2603224696 |

60 | ⁵√60 | 2.2679331553 |

61 | ⁵√61 | 2.2754430321 |

62 | ⁵√62 | 2.2828550557 |

63 | ⁵√63 | 2.2901720489 |

64 | ⁵√64 | 2.29739671 |

65 | ⁵√65 | 2.3045316198 |

66 | ⁵√66 | 2.3115792487 |

67 | ⁵√67 | 2.318541963 |

68 | ⁵√68 | 2.3254220304 |

69 | ⁵√69 | 2.3322216262 |

70 | ⁵√70 | 2.3389428374 |

71 | ⁵√71 | 2.3455876685 |

72 | ⁵√72 | 2.352158045 |

73 | ⁵√73 | 2.3586558182 |

74 | ⁵√74 | 2.3650827686 |

75 | ⁵√75 | 2.3714406098 |

76 | ⁵√76 | 2.3777309916 |

77 | ⁵√77 | 2.3839555035 |

78 | ⁵√78 | 2.3901156774 |

79 | ⁵√79 | 2.3962129905 |

80 | ⁵√80 | 2.402248868 |

81 | ⁵√81 | 2.4082246853 |

82 | ⁵√82 | 2.4141417706 |

83 | ⁵√83 | 2.420001407 |

84 | ⁵√84 | 2.4258048343 |

85 | ⁵√85 | 2.4315532515 |

86 | ⁵√86 | 2.437247818 |

87 | ⁵√87 | 2.4428896557 |

88 | ⁵√88 | 2.4484798507 |

89 | ⁵√89 | 2.4540194545 |

90 | ⁵√90 | 2.4595094858 |

91 | ⁵√91 | 2.4649509317 |

92 | ⁵√92 | 2.470344749 |

93 | ⁵√93 | 2.4756918656 |

94 | ⁵√94 | 2.4809931816 |

95 | ⁵√95 | 2.4862495702 |

96 | ⁵√96 | 2.4914618792 |

97 | ⁵√97 | 2.4966309317 |

98 | ⁵√98 | 2.5017575271 |

99 | ⁵√99 | 2.5068424421 |

100 | ⁵√100 | 2.5118864315 |

Ahead is the bottom line.

## Conclusion

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Note that you can find the value of many 5th roots by using the search form in the header menu.

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