How to Put Cubed Root in Graphing Calculator

Graphing calculators are powerful tools for solving mathematical problems, including finding roots of numbers. The cubed root of a number is a value that, when multiplied by itself three times, gives the original number. This guide will show you how to properly input and calculate cubed roots in your graphing calculator.

How to Enter Cubed Root in a Graphing Calculator

Entering a cubed root in a graphing calculator depends on the specific model you're using, but most scientific and graphing calculators follow similar steps. Here's a general guide:

Step 1: Access the Math Menu

Most graphing calculators have a dedicated math menu where you can find special functions. Look for a button labeled "MATH" or "FUNC".

Step 2: Find the Root Function

In the math menu, look for a section labeled "Root" or "Radical". Some calculators may have separate options for square roots and nth roots.

Step 3: Select Cubed Root

If your calculator has a dedicated cubed root function, select it. If it only has an nth root function, you'll need to specify the exponent as 3.

Step 4: Enter the Number

After selecting the root function, enter the number you want to find the cubed root of. For example, if you want to find the cubed root of 27, you would enter 27.

Step 5: Execute the Calculation

Press the equals (=) button or the execute button to perform the calculation. The calculator should display the result, which should be 3 in this case.

Tip

If your calculator doesn't have a dedicated cubed root function, you can calculate it using the exponent function (y^x) by raising the number to the power of 1/3.

The Formula for Cubed Root

The mathematical formula for the cubed root of a number x is:

Cubed Root Formula

∛x = x^(1/3)

This means the cubed root of x is equal to x raised to the power of 1/3. For example:

∛8 = 8^(1/3) = 2
∛27 = 27^(1/3) = 3
∛1000 = 1000^(1/3) = 10

This formula works for both positive and negative numbers, though the result for negative numbers will also be negative.

Worked Examples

Example 1: Finding ∛64

To find the cubed root of 64:

Access the math menu on your calculator
Select the cubed root function
Enter 64
Press equals

The calculator should display 4, since 4 × 4 × 4 = 64.

Example 2: Finding ∛-216

To find the cubed root of -216:

Access the math menu on your calculator
Select the cubed root function
Enter -216
Press equals

The calculator should display -6, since -6 × -6 × -6 = -216.

Example 3: Using the Exponent Method

If your calculator doesn't have a dedicated cubed root function, you can use the exponent method:

Access the exponent function (y^x)
Enter 100 as the base
Enter 1/3 as the exponent
Press equals

The calculator should display approximately 4.6416, which is the cubed root of 100.

FAQ

What is the difference between square root and cubed root?

A square root of a number x is a value that, when multiplied by itself, gives x. A cubed root is a value that, when multiplied by itself three times, gives x. The square root symbol is √, while the cubed root symbol is ∛.

Can I find the cubed root of a negative number?

Yes, you can find the cubed root of a negative number. The result will also be negative. For example, ∛(-8) = -2 because (-2) × (-2) × (-2) = -8.

What if my calculator doesn't have a cubed root function?

If your calculator doesn't have a dedicated cubed root function, you can use the exponent function to calculate it. Simply raise the number to the power of 1/3 (x^(1/3)).

How accurate are the results from a graphing calculator?

Graphing calculators provide highly accurate results for basic mathematical operations. For most practical purposes, the results will be precise enough. However, for very large or very small numbers, you might need to consider the limitations of floating-point arithmetic.