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How to Put 4th Root in Calculator

Reviewed by Calculator Editorial Team

Calculating the 4th root of a number is a common mathematical operation that can be performed using a calculator. This guide explains how to input and compute the 4th root on various calculator types, including scientific and graphing calculators.

How to Calculate the 4th Root

The 4th root of a number x is a value that, when raised to the power of 4, gives the original number x. Mathematically, it's represented as x^(1/4).

To find the 4th root of a number using a calculator, follow these steps:

  1. Enter the number you want to find the 4th root of.
  2. Locate the exponent or power function on your calculator.
  3. Input the exponent value of 1/4 or use the root function if available.
  4. Press the equals button to compute the result.

Different calculators may have slightly different interfaces, but the basic principle remains the same.

The Formula Explained

The mathematical formula for the 4th root of a number x is:

4th Root Formula

4th root of x = x^(1/4)

This formula means that the 4th root of x is the number which, when multiplied by itself four times, equals x.

For example, the 4th root of 16 is 2 because 2 × 2 × 2 × 2 = 16.

Using a Calculator

Most scientific and graphing calculators have a dedicated root function or an exponent function that can be used to calculate the 4th root. Here's how to do it on different types of calculators:

Scientific Calculator

  1. Enter the number you want to find the 4th root of.
  2. Press the "y^x" or exponent button.
  3. Enter "1/4" or "0.25" as the exponent.
  4. Press the equals button to get the result.

Graphing Calculator

  1. Enter the number in the calculator's memory.
  2. Use the exponent function or root function if available.
  3. For the exponent method, enter the number followed by "^(1/4)".
  4. Execute the calculation to get the 4th root.

Online Calculator

  1. Enter the number in the input field.
  2. Select the "4th root" function from the options.
  3. Click the calculate button to get the result.

Tip

If your calculator doesn't have a dedicated root function, you can use the exponent function with 1/4 as the exponent to calculate the 4th root.

Worked Examples

Let's look at some examples of calculating the 4th root using a calculator.

Example 1: 4th Root of 16

  1. Enter 16 on the calculator.
  2. Press the exponent button and enter 1/4.
  3. The result should be 2.

Verification: 2 × 2 × 2 × 2 = 16

Example 2: 4th Root of 81

  1. Enter 81 on the calculator.
  2. Press the exponent button and enter 1/4.
  3. The result should be approximately 2.9999 (which is very close to 3).

Verification: 3 × 3 × 3 × 3 = 81

Example 3: 4th Root of 10000

  1. Enter 10000 on the calculator.
  2. Press the exponent button and enter 1/4.
  3. The result should be 10.

Verification: 10 × 10 × 10 × 10 = 10000

Note

For non-perfect fourth powers, the calculator will give an approximate decimal result. The actual value may be slightly different due to rounding in the calculation.

FAQ

Can I calculate the 4th root without a calculator?

Yes, you can use the formula x^(1/4) and perform the calculation manually, but it's more time-consuming and prone to errors. A calculator is the most efficient method.

What if the number doesn't have a perfect 4th root?

The calculator will provide an approximate decimal result. For example, the 4th root of 10 is approximately 1.7783.

Is the 4th root the same as the square root of the square root?

Yes, the 4th root of a number is equivalent to taking the square root of the square root of that number. Mathematically, √(√x) = x^(1/4).

Can I calculate the 4th root of a negative number?

No, the 4th root of a negative number is not a real number. Calculators will typically display an error message for negative inputs when calculating roots.