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How to Write A Cube Root on A Calculator

Reviewed by Calculator Editorial Team

Calculating cube roots is a common mathematical operation, and knowing how to write them properly on a calculator ensures accurate results. This guide explains the different methods for entering cube roots on calculators, including scientific and graphing models, and provides examples to help you understand the process.

How to Write a Cube Root

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. The symbol for cube root is ∛ (the radical symbol with a small 3 in the top left corner).

Formula: ∛a = b, where b × b × b = a

Basic Notation

To write a cube root, you use the radical symbol (√) with a small 3 in the top left corner. For example:

  • ∛8 = 2 (because 2 × 2 × 2 = 8)
  • ∛27 = 3 (because 3 × 3 × 3 = 27)

Exponent Form

Cube roots can also be written using exponents. The cube root of a is equivalent to a raised to the power of 1/3:

∛a = a^(1/3)

This form is particularly useful when using scientific calculators that support exponentiation.

Calculator Methods

Different calculators have different ways of entering cube roots. Here are the most common methods:

Scientific Calculators

Most scientific calculators have a dedicated cube root function. Look for a button labeled "x³" or "³√".

  1. Enter the number you want to find the cube root of.
  2. Press the cube root function button.
  3. The calculator will display the result.

Graphing Calculators

Graphing calculators often require you to use the exponent form:

  1. Enter the number (e.g., 27).
  2. Press the exponentiation button (^ or x^y).
  3. Enter the exponent (1/3).
  4. Press the equals button to get the result (3).

Programmable Calculators

For programmable calculators, you can write a custom function or use the exponent method.

Tip: If your calculator doesn't have a cube root function, use the exponent method (a^(1/3)) for accurate results.

Examples

Let's look at some examples of how to calculate cube roots on a calculator.

Example 1: ∛64

  1. Enter 64 on your calculator.
  2. Press the cube root button (³√).
  3. The result is 4 (because 4 × 4 × 4 = 64).

Example 2: ∛125

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

Example 3: Using Exponent Form

If your calculator doesn't have a cube root button, use the exponent method:

  1. Enter 8.
  2. Press the exponentiation button (^ or x^y).
  3. Enter 1/3.
  4. Press the equals button to get the result (2).

FAQ

What is the difference between a square root and a cube root?

A square root is a number that, when multiplied by itself, gives the original number (√a = b, where b × b = a). A cube root is a number that, when multiplied by itself three times, gives the original number (∛a = b, where b × b × b = a).

How do I calculate a cube root on a calculator without a dedicated button?

If your calculator doesn't have a cube root button, you can use the exponent method: enter the number, press the exponentiation button, enter 1/3, and then press equals.

What is the cube root of a negative number?

The cube root of a negative number is also negative. For example, ∛(-8) = -2 because (-2) × (-2) × (-2) = -8.

Can I calculate cube roots on my smartphone calculator?

Yes, most smartphone calculators have a cube root function. Look for the "x³" or "³√" button. If it's not available, use the exponent method (a^(1/3)).