With a little practice, you may get pretty good at spotting the cube roots of easy numbers. For example, 3√8 = 2, 3√27 = 3 and so on. But when it comes to finding cube roots for larger numbers, or finding exact values for cube roots that don't work out to a whole number, a scientific calculator becomes a very useful tool. If you're using a calculator with graphing capability, you can also access a graph of this function.
Finding a Cube Root on a TI-83/84 Calculator
The TI-83/84 series of calculators is the most popular graphing calculator you may encounter in academic settings, and all models use the same process to access cube roots.
Press the MATH key, located on the far left side of the calculator, to bring up a menu of special operations.
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Press 4 to select the cube root function, then input the number you'd like to find the cube root of and press ENTER. The calculator will return the value of the cube root.
Graphing a Cube Root on a TI-83/84 Calculator
Again, all versions of the TI-83/84 graphing calculator use a similar process to generate a graph of the cube root function.
Press the y = key, located in the top left corner of the calculator, to access the graphing menu.
Press MATH to bring up the menu of special operations, then press 4 to select the cube root function. Next, press the "X, T, θ, n" key, located to the left of the arrow keypad, which generates an x under the cube root function. (In other words, you're asking the calculator to graph 3√x.)
Press the GRAPH key, located in the upper right corner of the calculator. This generates a graph of the cube root function.
Finding a Cube Root on a Casio FX Graphing Calculator
Another very popular graphing calculator, the Casio FX series (which includes the FX-9860GII and the FX-9750GII), allows you to access the cube root function straight from the main keypad.
Press the SHIFT key, followed by the ( key. This activates the cube root function.
Enter the number you want to find the cube root of, then hit EXE (execute) to return the result.
Graphing a Cube Root on a Casio FX Graphing Calculator
You can also use the Casio FX series' graphing capability to show a graph of the cube root function.
Press the MENU key, then use the arrow keys to navigate to GRAPH mode. Press EXE to enter graph mode.
Enter the cube root function as just described, with one small difference: Press SHIFT, followed by the ( key, to create the cube root function. Then press the "x, θ, T" key, located on the far left side of the calculator keypad, to enter an x under the cube root sign.
Press F6 to generate the graph of the cube root function.
When You Might Use Cube Roots
The most obvious place you'll use this sort of calculation is in algebra problems. For example, if you're given the equation x3 = 125, you'll need to use the cube root function to solve for x. In the real world, cube roots pop up when you consider problems in three dimensions or, to put it another way, when you start calculating volume.
For example, if you're trying to figure out the dimensions of a square-shaped container whose volume you already know, you could use the cube root function to find the length of its sides. That's because the volume of a square container is y3 or y × y × y, where y is the length of one of its sides. So if you already know the volume V, you calculating 3√V gives you the length of each side.