Lesson 3

Discover

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

Try This 1

1. Use a calculator to see whether the square root of a number multiplied by the square root of another number is equal to the square root of the product of the numbers. In simple terms, is true?
   
   
   • Try some of the common numbers provided in the chart until you think you know the answer.
     
     
   • Enter some of your own numbers to check.
     
     
   • If you prefer, you may use a spreadsheet to do these calculations.
     
   
   
    

   a	b	(to two decimal places)	(to two decimal places)
   1	10
   2	9
   3	8
   4	7
   5	6
   6	4
   7	3
   8	5
   9	4

   
   
   
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 determine whether . In words, is the square root of some number divided by the square root of another number equal to the square root of the quotient of the two numbers? Try some of the common numbers in the chart until you think you know the answer. Enter some of your own numbers to check.
   
   
    

   a	b	(to two decimal places)	(to two decimal places)
   10	2
   9	3
   8	4
   7	5
   6	6
   4	7
   3	8
   5	9
   4	10

   
   
   
5. What do you conclude? Is ?

Save your work in your course folder.

Share 1

1. Based on your observations from Try This 1, discuss the following questions with a partner or group.
   
   
   1. Is ?
      
      
   2. Is ?
      
      
2. Summarize your discussion by creating a general rule about multiplying square roots and another rule about dividing square roots.

Save your work in your course folder.