How to Take A Fourth Root on A Calculator

Calculating the fourth root of a number is a common mathematical operation that can be performed using a calculator. This guide explains how to find the fourth root using different methods, including step-by-step instructions for using a calculator.

How to Calculate the Fourth Root

The fourth root of a number x is a value that, when raised to the power of 4, equals x. Mathematically, it's represented as:

x^(1/4) = y

where y^4 = x

For example, the fourth root of 16 is 2 because 2 × 2 × 2 × 2 = 16. There are several methods to calculate the fourth root, including using a calculator, manual methods, and programming functions.

Using a Calculator

Most scientific and graphing calculators have a function to calculate roots. Here's how to find the fourth root using a calculator:

Enter the number you want to find the fourth root of.
Press the "y^x" or "exponent" button (often labeled as ^ or x^y).
Enter "0.25" (which is 1/4) or use the fraction function if available.
Press the equals (=) button to get the result.

Note: Some calculators may have a dedicated "nth root" function. If available, you can use that by entering 4 as the root and the number as the radicand.

Manual Calculation

If you don't have a calculator, you can estimate the fourth root using the following steps:

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

For example, to find the fourth root of 81:

Square root of 81 is 9.
Square root of 9 is 3.

Therefore, the fourth root of 81 is 3.

Worked Examples

Let's look at a few examples of calculating fourth roots:

Example 1: Fourth Root of 16

16^(1/4) = 2 because 2 × 2 × 2 × 2 = 16.

Example 2: Fourth Root of 81

81^(1/4) = 3 because 3 × 3 × 3 × 3 = 81.

Example 3: Fourth Root of 16.79616

16.79616^(1/4) ≈ 2.4 because 2.4 × 2.4 × 2.4 × 2.4 ≈ 16.79616.

FAQ

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

A square root is the value that, when multiplied by itself, gives the original number. A fourth root is the value that, when multiplied by itself four times, gives the original number.

Can I calculate 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.

How do I calculate the fourth root of a fraction?

You can calculate the fourth root of a fraction by first converting it to a decimal, then using the same method as for whole numbers.