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How to Write A Cube Root Into A Calculator

Reviewed by Calculator Editorial Team

Calculating cube roots is a fundamental math operation that appears in many fields including algebra, geometry, and physics. This guide explains how to properly write and calculate cube roots on different types of calculators.

How to Enter a Cube Root

The method for entering a cube root varies slightly depending on your calculator type. Here are the most common approaches:

Scientific Calculators

  1. Press the "x²" or "y^x" button to access exponent functions
  2. Enter the number you want to find the cube root of
  3. Press the "1/3" or "1/x" button to indicate the reciprocal exponent
  4. Press "=" to calculate the result

Graphing Calculators

  1. Access the math menu and select "Math" or "Functions"
  2. Choose the cube root function (often labeled as "³√x")
  3. Enter the number inside the parentheses
  4. Execute the function

Programmable Calculators

  1. Use the exponentiation function with 1/3 as the exponent
  2. For example: "2^(1/3)" for the cube root of 2
  3. Store the result in a variable if needed

Note: Some older calculators may require you to use logarithms to calculate cube roots. The formula is: ³√a = 10^(log₁₀a / 3)

Different Calculator Types

Understanding your calculator's capabilities is key to accurate cube root calculations:

Basic Calculators

Basic calculators typically don't have a dedicated cube root function. You'll need to use the exponent function with 1/3 as the exponent.

Scientific Calculators

Scientific calculators usually have a direct cube root function (³√x) or an exponent function that can be used with 1/3 as the exponent.

Graphing Calculators

Graphing calculators often have advanced math functions including cube roots, which can be accessed through the math menu.

Programmable Calculators

Programmable calculators allow you to create custom functions for cube roots, giving you more flexibility in calculations.

³√a = a^(1/3)

Cube Root Formula

The cube root of a number a is a value that, when multiplied by itself three times, gives the original number a. Mathematically, this is represented as:

³√a = b

where b × b × b = a

For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27.

Using Exponents

The cube root can also be expressed using exponents:

³√a = a^(1/3)

This means you can calculate cube roots by raising the number to the power of 1/3.

Worked Examples

Example 1: Cube Root of 8

  1. Enter 8 on your calculator
  2. Press the exponent button (y^x)
  3. Enter 1/3
  4. Press "=" to get the result: 2

Example 2: Cube Root of 216

  1. Enter 216 on your calculator
  2. Use the cube root function (³√x)
  3. Press "=" to get the result: 6

Example 3: Cube Root of 0.008

  1. Enter 0.008 on your calculator
  2. Press the exponent button (y^x)
  3. Enter 1/3
  4. Press "=" to get the result: 0.2

Remember: Cube roots of negative numbers are negative. For example, ³√(-8) = -2.

FAQ

What is the difference between a square root and a cube root?
A square root finds a number that, when multiplied by itself, gives the original number. A cube root finds a number that, when multiplied by itself three times, gives the original number.
Can I calculate cube roots without a calculator?
Yes, you can estimate cube roots by finding numbers that, when multiplied together three times, get close to your target number.
What happens if I try to find the cube root of a negative number?
The cube root of a negative number is negative. For example, ³√(-27) = -3.
Is there a difference between cube roots and cube functions?
Yes, cube functions (x³) multiply a number by itself three times, while cube roots find a number that, when multiplied three times, gives the original number.
Can I use logarithms to calculate cube roots?
Yes, you can use the formula ³√a = 10^(log₁₀a / 3) on calculators that don't have a direct cube root function.