How to Take The Fourth Root on A Calculator

The fourth root of a number is a value that, when raised to the power of 4, gives the original number. This guide explains how to calculate the fourth root using a calculator and provides practical examples.

What is the Fourth Root?

The fourth root of a number x is a number y such that y⁴ = x. For example, the fourth root of 16 is 2 because 2 × 2 × 2 × 2 = 16.

Fourth roots are used in various mathematical applications, including solving equations, calculating volumes, and analyzing data distributions.

Fourth Root Formula

For a positive real number x, the fourth root can be expressed as:

y = x^(1/4)

Using a Calculator

Most scientific calculators have a dedicated fourth root function or can compute it using exponentiation. Here's how to use a calculator:

Enter the number you want to find the fourth root of.
Press the exponentiation key (often labeled as "yˣ" or "^").
Enter "0.25" (since 1/4 = 0.25).
Press the equals (=) key to get the result.

Note

If your calculator doesn't have a fourth root function, you can use the exponentiation method described above.

Manual Calculation

If you need to calculate the fourth root without a calculator, you can use the following steps:

Find the square root of the number.
Then find the square root of the result from step 1.

For example, to find the fourth root of 16:

Square root of 16 is 4.
Square root of 4 is 2.

The result is 2, which is the fourth root of 16.

Real-World Examples

Fourth roots have practical applications in various fields:

Volume Calculation

If you have a cube with a volume of 16 cubic units, the length of each side is the fourth root of 16, which is 2 units.

Financial Analysis

In finance, fourth roots can be used to analyze compound growth rates when dealing with quarterly compounding periods.

Data Analysis

In statistics, fourth roots are sometimes used in measures of skewness to analyze data distributions.

FAQ

Can I find the fourth root of a negative number?

No, the fourth root of a negative number is not a real number. It's only defined for non-negative real numbers.

What's the difference between square root and fourth root?

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

How accurate are calculator results for fourth roots?

Modern calculators provide highly accurate results for fourth roots, typically to at least 10 decimal places.