How to Write Cube Root on A Graphing Calculator

Graphing calculators are powerful tools for solving mathematical problems, including finding cube roots. This guide explains how to properly write cube root expressions on various graphing calculator models, with practical examples and a built-in calculator.

Basic Syntax for Cube Root

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. On graphing calculators, cube roots are typically written using the caret (^) symbol or the dedicated cube root function.

Formula

Cube root of x: x^(1/3) or ∛x

Most modern graphing calculators support both notations. The caret notation (x^(1/3)) is more universally compatible across different calculator models, while the radical notation (∛x) is more intuitive but may not work on all older models.

Note

Some calculators may require you to use parentheses around the exponent (1/3) to ensure proper order of operations.

Examples on Different Calculators

Here are examples of how to write cube roots on different popular graphing calculator models:

TI-84 Plus CE

To find the cube root of 27 on a TI-84 Plus CE:

Press the [MATH] key
Select option 1: "mathProb"
Select option 1: "cubeRoot("
Enter the number (27)
Close the parentheses with [)]
Press [ENTER]

Casio fx-CG50

To find the cube root of 27 on a Casio fx-CG50:

Press the [SHIFT] key
Press the [∛] key
Enter the number (27)
Press [=]

HP Prime

To find the cube root of 27 on an HP Prime:

Press the [x^(1/3)] key
Enter the number (27)
Press [ENTER]

Advanced Usage

Beyond simple cube roots, you can combine them with other operations:

Nested Cube Roots

To find the cube root of a cube root:

∛(∛(27)) = 3^(1/9)

Cube Roots with Variables

When working with variables, you can write:

∛x or x^(1/3)

Complex Cube Roots

For complex numbers, the cube root function will return the principal root:

∛(-8) = -2

Common Mistakes to Avoid

When writing cube roots on graphing calculators, avoid these common errors:

Incorrect Syntax

Some calculators require specific syntax. For example, on older models, you might need to use:

1/3 * log(x)

instead of the direct cube root notation.

Missing Parentheses

For complex expressions, ensure all parentheses are properly closed. For example:

∛(x + 5) is correct, while ∛x + 5 is incorrect

Domain Errors

Cube roots are defined for all real numbers, but some calculators may show errors for complex numbers unless you're using a calculator that supports complex arithmetic.

FAQ

Can I use the cube root function on all graphing calculators?: Most modern graphing calculators support cube roots, but older models may require different syntax. Check your calculator's manual for specific instructions.
What happens if I try to find the cube root of a negative number?: On most calculators, the cube root of a negative number will return the negative root. For example, ∛(-8) = -2.
How do I find the cube root of a fraction?: You can write the fraction as a decimal or keep it as a fraction. For example, ∛(1/8) = 1/2 or 0.5.
Can I use the cube root function in equations?: Yes, you can use cube roots in equations. For example, to solve x = ∛(27), you would enter 27^(1/3) or use the dedicated cube root function.
What if my calculator doesn't have a cube root button?: You can use the exponent notation x^(1/3) instead. This works on most scientific and graphing calculators.