10.2.3 Calculator Exploration: Cube Roots and More

In this exploration, you will use the calculator to find cube roots and other types of roots.

Calculator IconThe calculator can be accessed on the left-hand side bar under Toolkit.

4 is a square root of 16 because four multiplication four equals 16. 3 is a cube root of 27 because three multiplication three multiplication three equals 27, and 2 is a fourth root of 16 because two multiplication two multiplication two multiplication two equals 16.

The type of root is determined by the number of identical factors that make up the product: two identical factors are square roots, three identical factors are cube roots, four identical factors are fourth roots, and so on.

Identifying cube roots and other roots is not easy, so the calculator is very useful. Cube, fourth, fifth, and any other roots are found using the The y-th root button key. The image below shows where to locate this key on the calculator.

Cube roots and higher roots are a bit trickier than square roots to input into the calculator. Check that the cube root of 27 is 3 by entering the following: Press the yth root button followed by 27, a comma, the number 3 and a parentheses closed, then equals..

Before you click the Equals key, you should see this:

In the white window you see sqrt (27, 3), which the calculator uses as shorthand for the cube root of 27. If you find this confusing, then watch the black window, where you can see the correctly formatted cube root. Clicking on the Equals key gives the answer 3.

Let’s do another example for extra practice. See if you can work out the method by entering the following to find root of order four over four.

The button sequence is similar to the one used above, so you should enter the following: Press the yth root button followed by 16, a comma, the number 4 and a parentheses closed, then equals..

Before you click the Equals key, you should see this:

Once again the white window will display special notation, but you can just look at the black window to verify that the calculator is computing the fourth root of 16. Clicking on the Equals key gives the answer 2.

Activity Symbol Activity: Cube Roots and More

(a) Use the calculator to find the cube root of 4,913. Check your answer by cubing it.

Hint Symbol

Comment

Take your time entering each calculation, watching the windows to make sure that you are entering everything correctly. Remember that after you use the The button shown is the y-th root key. key, you will need to type in the number you are taking the root of, followed by which root you want to take, separated by a comma.

To check your work, take the answer given by the calculator and raise it to the root as a power using the The button shown is the the y-th power key. key.

Solution Symbol

Answer

(a) The cube root of 4,913 is 17. You can check this by finding 17 cubed equals 4913.

Screen shot showing cube root of 4913 equals 17 in the black display window and the white window underneath showing 17. Screen shot showing 17 cubed equals 4913 in the black display window and the white window underneath showing 4913.

(b) Use the calculator to find the fifth root of 7,776. Check your answer by raising it to the power 5.

Solution Symbol

Answer

(b) The fifth root of 7,776 is 6. You can check this by finding six super five equals 7776.

Screen shot showing fifth root of 7776 equals 6 in the black display window and the white window underneath showing 6. Screen shot showing 6 to the 5th power equals 7776 in the black display window and the white window underneath showing 7776.

To recap:

  • To find a cube, fourth, fifth, or any other root, use the The button shown is the y-th root key. key. Enter the number you want to find the root of, followed by a comma, and then the root required. Then, close the parentheses, and press the Equals key to see the answer.
  • To check your solution, use the The button shown is the y-th power key. key. Enter the answer you found, and raise it to the root as a power. Then, close the parentheses, and press the equals key to see the answer.

The last two sections have introduced new notation and new ways of manipulating numbers written in scientific notation as well as the roots of numbers. If you have not already done so, look back through these sections and summarize the key points in your math notebook before moving to the next section.

10.2.2 Repeating Square Roots

10.3 Scale Diagrams