1. Lesson 2

1.4. Discover

Mathematics 20-1 Module 5

Module 5: Radicals

 

Discover

 

In this section you will investigate the validity of the following statements:



Try This 1
  1. Use a calculator to determine if the square root of a number plus the square root of another number is equal to the square root of the sum of the numbers. In other words, is ? Try some of the common numbers in the chart, and then try some numbers of your own.

    If you prefer, you may use a spreadsheet to do these calculations. hint

     
    a b

    (to two decimal places)

    (to two decimal places)
    1 2  
    2 2    
    3 2    
    4 2    
    5 2    
    3 3    
    4 3    
    5 3    
    6 3    
           
           
           
           


  2. As you were completing the columns for and , did you notice any patterns? If so, explain.

  3. Does ? Explain your reasoning.

  4. Use a calculator to verify if the following simplification is true:

     


    Try some of the common numbers in the chart, and then try some of your own numbers.

     
    a b x

    (to two decimal places)

    (to two decimal places)
    1 2 3    
    2 2 3    
    3 2 3    
    4 2 3    
    5 2 3    
    3 3 5    
    4 3 5    
    5 3 5    
    6 3 5    
             
             
             
             


  5. What do you conclude? Is ?

course folder Save your work in your course folder.

 

Share 1
  1. Based on your observations thus far, discuss the following questions with a partner or group.

    1. Is ?

    2. Is ?

  2. Summarize your discussion by creating a general rule about adding square roots.

course folder Save your work in your course folder.


Instructions for using a spreadsheet to take roots can be found by searching the Internet for “taking roots spreadsheet.” 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).

 

To avoid having 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.