How Do You Put The Fourth Root Into 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 input the fourth root function on different types of calculators and provides examples to help you understand the process.

How to Calculate the Fourth Root

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

Fourth Root Formula: ∜x = x^1/4

There are several methods to calculate the fourth root of a number:

Using a scientific calculator
Using a graphing calculator
Using a programming calculator
Manually using logarithms and exponents

Using a Calculator

Most scientific and graphing calculators have a function to calculate roots. Here's how to use it:

On a Scientific Calculator

Enter the number you want to find the fourth root of
Press the "y^x" or "x^y" button
Enter "0.25" (since 1/4 = 0.25)
Press "=" to get the result

On a Graphing Calculator

Enter the number in the input field
Use the "x^y" function and enter 0.25 as the exponent
Execute the function to get the result

On a Programming Calculator

Enter the number
Use the "x^y" function and input 0.25
Calculate to find the fourth root

Note: Some calculators may have a dedicated "n√x" function where you can enter 4 for the root value. Check your calculator's manual for specific instructions.

Manual Calculation

If you don't have a calculator, you can find the fourth root using logarithms and exponents:

Manual Calculation Formula: ∜x = 10^{(log x)/4}

Take the logarithm (base 10) of the number x
Divide the result by 4
Calculate 10 raised to the power of this result

This method is less precise than using a calculator but can be useful in situations where a calculator isn't available.

Examples

Let's look at some examples to understand how to calculate fourth roots:

Example 1: Finding the Fourth Root of 16

We want to find ∜16.

Using the formula: ∜16 = 16^1/4 = 2, because 2 × 2 × 2 × 2 = 16.

Example 2: Finding the Fourth Root of 81

We want to find ∜81.

Using the formula: ∜81 = 81^1/4 ≈ 3, because 3 × 3 × 3 × 3 = 81.

Example 3: Finding the Fourth Root of 100

We want to find ∜100.

Using the formula: ∜100 = 100^1/4 ≈ 3.162, because 3.162 × 3.162 × 3.162 × 3.162 ≈ 100.

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 (x^1/2). The fourth root is a value that, when multiplied by itself four times, gives x (x^1/4).
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?: To find the fourth root of a fraction, you can take the fourth root of the numerator and the denominator separately. For example, ∜(a/b) = (∜a)/(∜b).
What is the difference between a fourth root and an exponent of 0.25?: They are essentially the same. The fourth root of x is equivalent to x raised to the power of 0.25 (x^0.25).
How can I verify my fourth root calculation?: You can verify by raising your result to the power of 4. If you get back the original number, your calculation is correct.