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How to Plug Cube Root Into Calculator

Reviewed by Calculator Editorial Team

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. Calculating cube roots is essential in mathematics, engineering, and science. This guide explains how to plug cube roots into a calculator and interpret the results.

How to Calculate Cube Root

Calculating cube roots involves finding the number that, when raised to the power of three, equals the original number. Here's a step-by-step process:

  1. Identify the number you want to find the cube root of.
  2. Use a calculator with a cube root function or follow the manual calculation method.
  3. Enter the number into the calculator and select the cube root function.
  4. Press the equals button to get the result.
  5. Interpret the result and verify it by cubing the answer to ensure it matches the original number.

Note: Most scientific calculators have a cube root function, often represented by a radical symbol with a small 3 in the top left corner (³√x).

Calculator Methods

There are several ways to calculate cube roots using a calculator:

Using the Cube Root Function

Most scientific calculators have a dedicated cube root function. To use it:

  1. Turn on your calculator.
  2. Enter the number you want to find the cube root of.
  3. Press the cube root function button (³√x).
  4. Press the equals button to display the result.

Using Exponentiation

If your calculator doesn't have a cube root function, you can use exponentiation:

  1. Enter the number you want to find the cube root of.
  2. Press the exponentiation button (yˣ).
  3. Enter 1/3 as the exponent.
  4. Press the equals button to display the result.

Using the Logarithm Function

For more advanced calculations, you can use logarithms:

  1. Enter the number you want to find the cube root of.
  2. Press the logarithm button (log).
  3. Divide the result by 3.
  4. Press the 10ˣ button to get the cube root.

Formula

The cube root of a number x can be calculated using the following formula:

³√x = x^(1/3)

Where:

  • ³√x is the cube root of x
  • x is the number you want to find the cube root of
  • ^(1/3) represents raising x to the power of one-third

This formula is the mathematical representation of the cube root function.

Examples

Here are some examples of cube roots calculated using the formula:

Number (x) Cube Root (³√x) Verification (³√x)³
8 2 2³ = 8
27 3 3³ = 27
64 4 4³ = 64
125 5 5³ = 125
216 6 6³ = 216

These examples demonstrate how the cube root function works and how to verify the results.

FAQ

What is the difference between square root and cube root?

The square root of a number is a value that, when multiplied by itself, gives the original number. The cube root is a value that, when multiplied by itself three times, gives the original number. In mathematical terms, the square root is x^(1/2) and the cube root is x^(1/3).

How do I calculate the cube root of a negative number?

The cube root of a negative number is also negative. For example, the cube root of -8 is -2 because (-2) × (-2) × (-2) = -8. Most scientific calculators can handle negative numbers for cube roots.

What is the cube root of zero?

The cube root of zero is zero because 0 × 0 × 0 = 0. This is a fundamental property of cube roots.

Can I calculate cube roots without a calculator?

Yes, you can calculate cube roots manually using estimation and the binomial approximation method, but it's more time-consuming than using a calculator. Calculators provide quick and accurate results.