4th Root of 8

The 4th root of 8 is the number, which multiplied by itself 4 times, is 8. In other words, this number to the power of 4 equals 8.

Besides the real values of \sqrt[4]{8} along with an explanation, on this page you can also find what the elements of the 4th root of 8 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]{8} = \pm1.6817928305This 4th Root Calculator and Information is Really Cool! Click To TweetIf you have been looking for the 4th root of eight, then you are right here, too.

The term can be written as \sqrt[4]{8} \hspace{3 mm}or\hspace{3 mm} 8^{1/4}.

As the index 4 is even and 8 is greater than 0, 8 has two real 4th roots: \sqrt[4]{8}, which is positive and called principal 4th root of 8, and −\sqrt[4]{8}, which is negative.

Together, they are denominated as ±\sqrt[4]{8}.

Although the principal fourth root of eight is only one of the two 4th roots, the term “4th root of 8” 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 8

Extracting the 4th root is the inverse operation of ^4:\underbrace{ {\rm \sqrt[4]{8} \times\thinspace ... \times\thinspace \sqrt[4]{8}} }_{\rm 4 \thickspace times} = \sqrt[4]{8}^{4}= 8In the following paragraph, we are going to name the elements of this ∜.

What is the 4th Root of 8?

You already have the answer to that question, and you also know about the inverse operation of 8 4th root.

Keep reading to learn what the parts are called.

  • \sqrt[4]{8} is the 4th root of 8 symbol
  • 4 is the index
  • 8 = radicand; the radicand is the number below the radical sign
  • 4th root = ±1.6817928305
  • √ is called radical symbol or radical only

4th root of 8 = ±1.6817928305

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

Now you really know all about \sqrt[4]{8}, 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. 8); the calculation is done automatically.

If you like our information about \sqrt[4]{8}, then a similar 4th root you may be interested in is, for example: 4th root of 10.

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

Table

The aim of this table is to provide you with an overview of the nth roots of 8.
IndexRadicandRootSymbolValue
28Square Root of 8\sqrt[2]{8}±2.8284271247
38Cube Root of 8\sqrt[3]{8}2
48Forth Root of 8\sqrt[4]{8}±1.6817928305
58Fifth Root of 8\sqrt[5]{8}1.5157165665
68Sixth Root of 8\sqrt[6]{8}±1.4142135624
78Seventh Root of 8\sqrt[7]{8}1.3459001926
88Eight Root of 8\sqrt[8]{8}±1.2968395547
98Nineth Root of 8\sqrt[9]{8}1.2599210499
108Tenth Root of 8\sqrt[10]{8}±1.2311444133
A few lines down from here we review the FAQs.

Fourth Root of Eight

If you have been searching for what's the fourth root of eight or 4-th root of 8, then you are reading the right post as well.

The same is true if you typed 4 root of 8 or 8 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 8

How Many Real Fourth Roots Does 8 Have?

8 has two real fourth roots, because the radicand 8 is positive and the index 4 is even.

What to the 4th Power Equals 8?

The 4th root of 8 to the power of 4 equals 8.

How Do You Find the Fourth Root of 8?

Start with an initial guess such that 4 times that value equals approximately 8, then keep improving the guess until you have the required precision.

What is 8 to the 4th Root?

8 to the 4th root = 8^1/4 = ±1.6817928305.

What Number is the 4th Root of 8?

The 4th root of 8 = ±1.6817928305.

How Do You Solve the 4-th Root of 8?

To compute the 4-th root of 8 use a calculator, and/or employ the Newton–Raphson method.

What is the Value of 4 Root 8?

The value of 4 root 8 is ±1.6817928305.



Ahead is the wrap-up of our information.

Summary

To sum up, the fourth roots of 8 are ±1.6817928305.

Finding the 4th root of the number 8 is the inverse operation of rising the \sqrt[4]{8} to the power of 4. That is to say, (±1.6817928305)4 = 8.

4th Root of 8
Further information related to \sqrt[4]{8} can be found on our page 4th Root.

Note that you can also locate roots like \sqrt[4]{8} by means of the search form in the menu and in the sidebar of this site.

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If you have any questions about the 4-th root of 8, fill in the comment form below.

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