1. Lesson 1

1.4. Discover

Mathematics 20-1 Module 5

Module 5: Radicals

 

Discover

 

This photo shows a radical (square root) button on a calculator keyboard.

iStockphoto/Thinkstock

In this section you will

  • investigate if or when it is possible to take the root of a negative number
  • develop rules about taking the root of a negative number
Try This 1

 

You will use a calculator to take various roots of +2000 and −2000. hint

 

If you prefer, you may use an applet or spreadsheet to do these calculations. hint

 

Complete Radicand Chart.

 

course folder Save your work in your course folder.

 

Share 1

 

Based on your observations from Try This 1, discuss the following questions with a partner or group.

  1. When is it possible to take the root of a negative number? Describe the patterns you see.

  2. How is this related to the multiplication of negative integers?

  3. Summarize your discussion by creating a general rule about taking the root of a negative number.

course folder Place a copy of this rule in your course folder.

Finding Roots of Numbers Using a Spreadsheet or Applet

 

If you prefer, you may use a spreadsheet to do these calculations. For directions on how to calculate a square root using a spreadsheet program, enter the keywords “taking roots spreadsheet” into an Internet search engine.

 

If you put the numbers into a spreadsheet in columns A and B, beginning in row 2, column C should be = SQRT(A2) + SQRT(B2), and column D should be = SQRT(A2 + B2).


So you don’t have to input the directions into every cell individually, click on cell C2 and drag the directions down 10 cells. Then hold down the Ctrl key and press D.

 

You can use the Ctrl + D feature to copy the instructions down each column as far as you wish.

Taking Roots with a Calculator

 

If your calculator has a “^” button, it means raise the preceding number to a power. Roots are rational powers. To take a cube root, raise a number to the exponent . For a fourth root, raise a number to the exponent . Enclose negative numbers and fractions in parentheses as shown.

 

This shows a cube root of a negative number.

 

If your calculator has an “xy” button, enter the number, press the “xy” button, and then enter the fractional exponent, in brackets, as . For example, if asked for the 5th root, enter the power as .