How to Put Cubed Root Into Desmos Online Calculator

Introduction

The cubed root of a number x, denoted as ∛x, is a value that, when multiplied by itself three times, gives the original number. In mathematical terms:

Desmos provides a user-friendly interface for working with mathematical expressions, including roots. This guide will show you how to implement and visualize cubed roots in Desmos.

Basic Cubed Root Calculation

To calculate a cubed root in Desmos, you can use the caret (^) operator or the built-in root function. Here are two equivalent ways to express a cubed root:

Both methods will give you the same result. The first method uses exponentiation with a fractional power, while the second method explicitly uses the root function with the degree specified.

Steps to Add Cubed Root in Desmos

1. Open Desmos

   Go to the Desmos website and open a new graph.

2. Enter the Expression

   In the left sidebar, you'll see a text input area. Enter your cubed root expression. For example:

   y = x^(1/3)

   Or if you prefer the root function:

   y = root(x, 3)

3. Adjust the Graph

   Desmos will automatically plot the function. You can adjust the graph by:

   • Zooming in/out with the mouse wheel
   • Panning by clicking and dragging
   • Adjusting the x and y ranges in the settings

4. Add Points or Sliders

   To make the graph interactive, you can add points or sliders:

   For a point:
   (a, b) = (2, 2^(1/3))

   For a slider:
   x = slider(1, 10, 1)

Advanced Usage

Once you're comfortable with basic cubed root calculations, you can explore more advanced applications:

• Comparing Roots

  You can compare square roots, cube roots, and other roots on the same graph:

  y1 = x^(1/2)
  y2 = x^(1/3)
  y3 = x^(1/4)

• Inverse Functions

  Create the inverse of the cubed root function:

  y = x^3

• Parametric Equations

  Use cubed roots in parametric equations for more complex shapes:

  x = t^3
  y = t^(1/3)

Troubleshooting

If you encounter issues with cubed roots in Desmos, try these solutions:

Why isn't my cubed root graph appearing?

Check that you've entered the expression correctly. Make sure there are no typos and that the parentheses are balanced. Also verify that the function is within the visible range of the graph.

How can I make the graph more accurate?

Adjust the graph's x and y ranges to focus on the area of interest. You can also increase the number of sample points in the settings for a smoother curve.

Can I use complex numbers with cubed roots?

Desmos supports complex numbers. For example, you can calculate the cube root of -8 as follows:

y = root(-8, 3)

This will give you the complex number 2e^(iπ/3).