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Fourth Root Calculator

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How to use this fourth root calculatorFourth root of a numberCalculating 4th rootOther toolsFAQs

Our fourth root calculator is a simple tool that will help you find the fourth root of a real number. You can even find any other root with this calculator!

In the following article, we shall learn what a fourth root is and how to calculate the fourth root of a real number.

How to use this fourth root calculator

Using our fourth root calculator is very simple:

  1. Enter the number a for which you need the fourth root.

  2. To find the fourth root of a, let the n parameter be equal to 4. Suppose you want to find a different root. Then input that value in the n parameter.

  3. The tool will instantly calculate the fourth root for you and give you the result.

For example, if you want to find the fourth root of 512, enter 512 in a, and let n be equal to 4. Instantly, you will get the result as 4.757.

To find the 3rd root of 512, enter 512 in a and change n from 4 to 3. Right away, the calculator will tell you that the third root of 512 is 8.

The following article will help you understand the math behind this calculator.

Fourth root of a number

To understand roots, let us first recall what exponent operation does — it raises a number bb to a given exponent (or power) nn, meaning that the number will be multiplied by itself nn times. We represent this operation as:

a=bn=b×b×b×...n timesa = b^n = b \times b \times b \times ...n \text{ times}

For instance, 3 raised to the power 4 is:

34=3×3×3×3=813^4 = 3 \times 3 \times 3 \times 3 = 81

The root operation functions as an inverse of the exponent operation — it finds the number bb that must be raised to the given power to produce the given number aa.

a=bnb=ana = b^n \Lrarr b = \sqrt[n]{a}

The fourth root of a number aa is the number bb that must be raised to the fourth power to produce aa.

In our earlier example, 3 is the fourth root of 81.

34=81    814=33^4 = 81 \implies \sqrt[4]{81} = 3

Calculating 4th root

Let's break down the 4th root calculation with an example problem - find the fourth root of 20736.

  1. Prime factorize the number 20736. Our prime factorization calculator can help you with this step.
20736=28×34\qquad 20736 = 2^8 \times 3^4
  1. Now, group these prime factors by sets of 4.
20736=(22)4×34\qquad 20736 = (2^2)^4 \times 3^4
  1. Apply the fourth root to the number in the prime factor form:
207364=(22)4×344=22×3=4×3207364=12\qquad \begin{align*} \sqrt[4]{20736} &= \sqrt[4]{(2^2)^4 \times 3^4}\\ &=2^2 \times 3 = 4 \times 3\\ \sqrt[4]{20736} &= 12 \end{align*}

Not all numbers' fourth root can be integers, of course! Calculating them can be a pain. But that's where our fourth root calculator can help you!😉 So what are you waiting for? Go and find some roots with our calculator!

Other tools

We have a couple of other root calculators for you:

FAQs

How can I calculate the fourth root of a real number?

To calculate the fourth root of a real number, follow these steps:

  1. Prime factorize the number.

  2. Group these prime factors by sets of 4.

  3. Apply the fourth root to the number in the prime factor form.

If you're having difficulty calculating the root manually, our fourth root calculator can help you.

What is the fourth root of 104976?

The fourth root of 104976 is 18. To arrive at this answer, follow these steps:

  1. Prime factorize the number 104976:
    104976 = 24 × 38.

  2. Group these prime factors by sets of 4:
    104976 = 24 × (32)4.

  3. Apply the fourth root to the number in the prime factor form:
    ∜(104976) = ∜(24 × (32)4) = 2 × 32 = 18.

Verify this result with our fourth root calculator.

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