How to Take The Fourth Root in 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 and provides practical examples.

How to Calculate the Fourth Root

The fourth root of a number is a value that, when raised to the power of 4, gives the original number. In mathematical terms, if y is the fourth root of x, then y⁴ = x.

To find the fourth root of a number using a calculator, follow these steps:

Enter the number for which you want to find the fourth root.
Press the "xⁿ" or "yˣ" button on your calculator (this is the exponent function).
Enter the exponent value of 0.25 (since 1/4 = 0.25).
Press the equals (=) button to get the result.

This method works for both positive and negative numbers, as the fourth root of a negative number is a real number.

Different Methods to Find the Fourth Root

Using the Exponent Function

The most straightforward method is using the exponent function on your calculator. As shown above, you raise the number to the power of 0.25.

Using Logarithms

For more advanced calculations, you can use logarithms. The formula is:

y = 10^(log₁₀(x)/4)

This method involves taking the logarithm of the number, dividing by 4, and then using the antilogarithm function.

Using Prime Factorization

For whole numbers, you can find the fourth root by prime factorization:

Factorize the number into its prime factors.
Group the prime factors into sets of four.
Take one factor from each group and multiply them together.

This method is more complex and typically used for educational purposes rather than practical calculations.

The Formula for Fourth Root

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

y = x^(1/4)

This formula can be implemented directly in most scientific calculators using the exponent function.

Note: The fourth root of a negative number is a real number. For example, the fourth root of -16 is -2 because (-2)⁴ = -16.

Worked Examples

Example 1: Positive Number

Find the fourth root of 16.

Enter 16 on your calculator.
Press the exponent function (xⁿ or yˣ).
Enter 0.25.
Press equals. The result is 2.

Verification: 2⁴ = 16, so the fourth root of 16 is indeed 2.

Example 2: Negative Number

Find the fourth root of -81.

Enter -81 on your calculator.
Press the exponent function.
Enter 0.25.
Press equals. The result is -3.

Verification: (-3)⁴ = (-3) × (-3) × (-3) × (-3) = 81, so the fourth root of -81 is -3.

FAQ

What is the difference between the square root and the 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 find the fourth root of a negative number?: Yes, you can find the fourth root of a negative number. The result will also be negative. For example, the fourth root of -16 is -2.
How do I find the fourth root of a fraction?: To find the fourth root of a fraction, you can use the exponent function on your calculator. For example, to find the fourth root of 1/16, enter 1/16, then raise it to the power of 0.25. The result will be 0.5.
What is the fourth root of zero?: The fourth root of zero is zero, because 0⁴ = 0.
How do I find the fourth root of a decimal number?: You can find the fourth root of a decimal number using the exponent function on your calculator. For example, to find the fourth root of 0.16, enter 0.16, then raise it to the power of 0.25. The result will be 0.7156 (approximately).