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How to Put Fourth Root in Calculator

Reviewed by Calculator Editorial Team

Calculating fourth roots is a common mathematical operation that finds applications in various fields. This guide explains how to perform fourth root calculations using both calculators and manual methods, along with practical examples and common uses.

How to Calculate Fourth Roots

The fourth root of a number is a value that, when raised to the power of 4, gives the original number. Mathematically, the fourth root of a number \( x \) is represented as \( \sqrt[4]{x} \).

Formula: \( \sqrt[4]{x} = x^{1/4} \)

There are two primary methods to calculate fourth roots: using a calculator and manual calculation. The following sections explain both approaches in detail.

Using a Calculator

Most scientific and graphing calculators have a built-in function to calculate roots. Here's how to use a calculator to find the fourth root of a number:

  1. Turn on your calculator and clear any previous calculations.
  2. Enter the number for which you want to find the fourth root.
  3. Locate the root function on your calculator. It is often labeled as "y√x" or "n√".
  4. Enter the root index, which is 4 for a fourth root.
  5. Press the equals (=) button to calculate the result.

Tip: If your calculator does not have a dedicated root function, you can use the exponent function by raising the number to the power of 1/4.

Example

Let's find the fourth root of 16 using a calculator:

  1. Enter 16 on the calculator.
  2. Press the root function and enter 4.
  3. The calculator will display 2, which is the fourth root of 16.

This method is quick and accurate for most practical purposes.

Manual Calculation

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

  1. Find the square root of the number. For example, the square root of 16 is 4.
  2. Take the square root of the result from step 1. For our example, the square root of 4 is 2.

Note: This method works because the fourth root of a number is the square root of its square root.

Example

Let's manually calculate the fourth root of 81:

  1. First, find the square root of 81, which is 9.
  2. Next, find the square root of 9, which is 3.
  3. Therefore, the fourth root of 81 is 3.

This method is useful for quick estimates but may not be as precise as using a calculator.

Common Uses of Fourth Roots

Fourth roots have several practical applications in various fields:

  • Mathematics: Fourth roots are used in solving equations and simplifying expressions.
  • Engineering: They are used in calculations involving volume and dimensions.
  • Physics: Fourth roots appear in calculations related to energy and power.
  • Finance: They are used in compound interest calculations and investment analysis.

Understanding how to calculate fourth roots is essential for anyone working in these fields.

FAQ

What is the difference between a square root and a fourth root?
The square root of a number is a value that, when multiplied by itself, gives the original number. The fourth root is a value that, when raised to the power of 4, gives the original number. Essentially, the fourth root is the square root of the square root.
Can I calculate the fourth root of a negative number?
No, the fourth root of a negative number is not a real number. It is an imaginary number, which is beyond the scope of this guide.
How do I calculate the fourth root of a fraction?
To calculate the fourth root of a fraction, you can use the same methods as for whole numbers. For example, the fourth root of 1/16 is 1/2.