How to Write Fourth Root on Calculator

Calculating the fourth root of a number is a common mathematical operation with practical applications in geometry, engineering, and finance. This guide explains how to write and calculate fourth roots using different calculator methods, provides the mathematical formula, and includes practical examples.

How to Calculate Fourth Root

The fourth root of a number x is a value that, when raised to the power of 4, gives x. In mathematical terms, the fourth root of x is written as ∜x or x^(1/4).

Step-by-Step Instructions

Identify the number for which you want to calculate the fourth root.
Use the calculator's exponent function or root function to compute the fourth root.
For calculators without a direct fourth root function, use the exponent function with 1/4 as the exponent.
Verify the result by raising the calculated fourth root to the power of 4 to ensure it equals the original number.

Important Note

The fourth root of a negative number is not a real number. If you attempt to calculate the fourth root of a negative number, the calculator will typically display an error message.

Calculator Methods

Most scientific and graphing calculators provide functions to calculate roots. Here are the common methods:

Using the Root Function

If your calculator has a dedicated root function, you can directly calculate the fourth root by selecting the root function and entering 4 as the index.

Using the Exponent Function

For calculators without a specific root function, use the exponent function (often marked as y^x or ^) and enter 1/4 as the exponent.

Using the Logarithm Function

Advanced calculators may allow you to use logarithms to calculate roots. The formula for the fourth root using logarithms is:

Formula

∜x = e^(ln(x)/4)

Formula

The mathematical formula for the fourth root of a number x is:

Fourth Root Formula

∜x = x^(1/4)

This formula states that the fourth root of x is equal to x raised to the power of 1/4.

Examples

Here are some examples of calculating fourth roots using different methods:

Example 1: Calculating ∜16

To calculate the fourth root of 16:

Enter 16 into your calculator.
Use the exponent function and enter 1/4 as the exponent.
The result should be 2, since 2^4 = 16.

Example 2: Calculating ∜81

To calculate the fourth root of 81:

Enter 81 into your calculator.
Use the exponent function and enter 1/4 as the exponent.
The result should be approximately 1.68179, since 1.68179^4 ≈ 81.

Example 3: Calculating ∜10000

To calculate the fourth root of 10,000:

Enter 10,000 into your calculator.
Use the exponent function and enter 1/4 as the exponent.
The result should be 10, since 10^4 = 10,000.

FAQ

What is the difference between a square root and a fourth root?

The square root of a number x is a value that, when multiplied by itself, gives x. The fourth root is a value that, when raised to the power of 4, gives x. Essentially, the fourth root is the square root of the square root of x.

Can I calculate the fourth root of a negative number?

No, the fourth root of a negative number is not a real number. Calculators will typically display an error message when attempting to calculate the fourth root of a negative number.

How do I calculate the fourth root using a basic calculator?

Basic calculators may not have a dedicated fourth root function. Instead, use the exponent function and enter 1/4 as the exponent. For example, to calculate ∜16, enter 16, then press the exponent button, enter 1, then the division button, and finally 4.

What is the relationship between the fourth root and exponents?

The fourth root of a number x is equivalent to raising x to the power of 1/4. This means that x^(1/4) is the same as ∜x.