# 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.

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

4 is a **square** root of 16 because
. 3 is a **cube** root of 27 because
, and 2 is a **fourth** root of 16 because
.

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 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: .

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 .

The button sequence is similar to the one used above, so you should enter the following: .

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: Cube Roots and More

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

### 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 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 key.

### Answer

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

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

### Answer

(b) The fifth root of 7,776 is 6. You can check this by finding .

## To recap:

- To find a cube, fourth, fifth, or any other root, use the 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 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