4th Root of 81

The 4th root of 81 is the number, which multiplied by itself 4 times, is 81. In other words, this number to the power of 4 equals 81.

Besides the real values of \sqrt[4]{81} along with an explanation, on this page you can also find what the elements of the 4th root of 81 are called.

In addition to the terminology, we have a calculator you don’t want to miss:

Fourth Root Calculator

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\sqrt[4]{81} = \pm3This 4th Root Calculator and Information is Really Cool! Click To TweetIf you have been looking for the 4th root of eighty-one, then you are right here, too.

The term can be written as \sqrt[4]{81} \hspace{3 mm}or\hspace{3 mm} 81^{1/4}.

As the index 4 is even and 81 is greater than 0, 81 has two real 4th roots: \sqrt[4]{81}, which is positive and called principal 4th root of 81, and −\sqrt[4]{81}, which is negative.

Together, they are denominated as ±\sqrt[4]{81}.

Although the principal fourth root of eighty-one is only one of the two 4th roots, the term “4th root of 81” usually refers to the positive number.

If you want to know how to find the value of this root, then read our article 4th Root located in the header menu.

There, we also discuss the properties for index n = 4 by means of examples: multiplication, division, exponentiation etc.

Next, we have a look at the inverse function.

Inverse of 4th Root of 81

Extracting the 4th root is the inverse operation of ^4:\underbrace{ {\rm \sqrt[4]{81} \times\thinspace ... \times\thinspace \sqrt[4]{81}} }_{\rm 4 \thickspace times} = \sqrt[4]{81}^{4}= 81In the following paragraph, we are going to name the elements of this ∜.

What is the 4th Root of 81?

You already have the answer to that question, and you also know about the inverse operation of 81 4th root.

Keep reading to learn what the parts are called.

  • \sqrt[4]{81} is the 4th root of 81 symbol
  • 4 is the index
  • 81 = radicand; the radicand is the number below the radical sign
  • 4th root = ±3
  • √ is called radical symbol or radical only

4th root of 81 = ±3

As a sidenote: All values on this page have been rounded to ten decimal places.

Now you really know all about \sqrt[4]{81}, including its values, parts and the inverse.

If you need to extract the 4th root of any other real number use our calculator above.

Simply insert the number of which you want to find the 4th root (e.g. 81); the calculation is done automatically.

If you like our information about \sqrt[4]{81}, then a similar 4th root you may be interested in is, for example: 4th root of 83.

In the following table you can find the n-th root of 81 for n = 2,3,4,5,6,7,8,9,10.


The aim of this table is to provide you with an overview of the nth roots of 81.
281Square Root of 81\sqrt[2]{81}±9
381Cube Root of 81\sqrt[3]{81}4.3267487109
481Forth Root of 81\sqrt[4]{81}±3
581Fifth Root of 81\sqrt[5]{81}2.4082246853
681Sixth Root of 81\sqrt[6]{81}±2.0800838231
781Seventh Root of 81\sqrt[7]{81}1.8734440046
881Eight Root of 81\sqrt[8]{81}±1.7320508076
981Nineth Root of 81\sqrt[9]{81}1.6294982222
1081Tenth Root of 81\sqrt[10]{81}±1.5518455739
A few lines down from here we review the FAQs.

Fourth Root of Eighty-One

If you have been searching for what's the fourth root of eighty-one or 4-th root of 81, then you are reading the right post as well.

The same is true if you typed 4 root of 81 or 81 4 root in the search engine of your preference, just to name a few similar terms.

Right below you can find the frequently asked questions in the context.

FAQs About the 4th Root of 81

How Many Real Fourth Roots Does 81 Have?

81 has two real fourth roots, because the radicand 81 is positive and the index 4 is even.

What to the 4th Power Equals 81?

The 4th root of 81 to the power of 4 equals 81.

How Do You Find the Fourth Root of 81?

Start with an initial guess such that 4 times that value equals approximately 81, then keep improving the guess until you have the required precision.

What is 81 to the 4th Root?

81 to the 4th root = 81^1/4 = ±3.

What Number is the 4th Root of 81?

The 4th root of 81 = ±3.

How Do You Solve the 4-th Root of 81?

To compute the 4-th root of 81 use a calculator, and/or employ the Newton–Raphson method.

What is the Value of 4 Root 81?

The value of 4 root 81 is ±3.

Ahead is the wrap-up of our information.


To sum up, the fourth roots of 81 are ±3.

Finding the 4th root of the number 81 is the inverse operation of rising the \sqrt[4]{81} to the power of 4. That is to say, (±3)4 = 81.

4th Root of 81
Further information related to \sqrt[4]{81} can be found on our page 4th Root.

Note that you can also locate roots like \sqrt[4]{81} by means of the search form in the menu and in the sidebar of this site.

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