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Work Out Cube Root on 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. This guide explains how to find cube roots using a calculator, including step-by-step instructions, formulas, and practical examples.

How to Calculate Cube Root

Calculating cube roots is straightforward with the right tools. Here's how to do it using a calculator:

  1. Enter the number you want to find the cube root of in the calculator.
  2. Press the cube root function (often labeled as "x³√" or "³√x").
  3. Press the equals (=) button to get the result.

Most scientific calculators have a dedicated cube root function. If your calculator doesn't have this function, you can calculate the cube root by raising the number to the power of 1/3.

For example, to find the cube root of 27:

  1. Enter 27 on your calculator.
  2. Press the exponentiation key (often labeled as "xʸ" or "^").
  3. Enter 1/3 (or 0.333...).
  4. Press the equals (=) button to get the result: 3.

Cube Root Formula

The cube root of a number x can be expressed mathematically as:

³√x = y, where y × y × y = x

This means that the cube root of x is a number y such that when y is multiplied by itself three times, the result is x.

For example:

  • ³√8 = 2, because 2 × 2 × 2 = 8
  • ³√27 = 3, because 3 × 3 × 3 = 27
  • ³√64 = 4, because 4 × 4 × 4 = 64

Cube roots can also be expressed using exponents:

x^(1/3) = ³√x

Cube Root Examples

Here are some examples of calculating cube roots:

Example 1: Finding the Cube Root of 216

To find the cube root of 216:

  1. Enter 216 on your calculator.
  2. Press the cube root function (³√).
  3. Press the equals (=) button.
  4. The result is 6, because 6 × 6 × 6 = 216.

Example 2: Finding the Cube Root of 125

To find the cube root of 125:

  1. Enter 125 on your calculator.
  2. Press the cube root function (³√).
  3. Press the equals (=) button.
  4. The result is 5, because 5 × 5 × 5 = 125.

Example 3: Finding the Cube Root of 1000

To find the cube root of 1000:

  1. Enter 1000 on your calculator.
  2. Press the cube root function (³√).
  3. Press the equals (=) button.
  4. The result is 10, because 10 × 10 × 10 = 1000.

Cube Root Applications

Cube roots have several practical applications in mathematics and real-world scenarios:

  • Volume Calculations: Cube roots are used to find the side length of a cube when given its volume.
  • Engineering: Cube roots are used in calculations involving cubic dimensions and volumes.
  • Finance: Cube roots are used in certain financial calculations and growth rate analyses.
  • Physics: Cube roots are used in calculations involving cubic relationships and proportionalities.

For example, if you know the volume of a cube is 216 cubic units, you can find the length of one side by taking the cube root of 216, which gives you 6 units.

FAQ

What is the cube root of a number?
The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27.
How do I calculate the cube root of a number?
You can calculate the cube root of a number using a calculator by entering the number and pressing the cube root function (³√). Alternatively, you can raise the number to the power of 1/3.
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.
Can I find the cube root of a negative number?
Yes, you can find the cube root of a negative number. For example, the cube root of -8 is -2 because (-2) × (-2) × (-2) = -8.
Where are cube roots used in real life?
Cube roots are used in various real-life applications, including volume calculations, engineering, finance, and physics. They are particularly useful when dealing with cubic dimensions and volumes.