Author: Kathy Halverson
Last saved by: Glencoe Mathematics
Company: Halverson Household

Lesson 9-1

Example 1	Find Square Roots
Find each square root.
a. 	 indicates the positive square root of 25.
      Since 5^2 = 25,  = 5.

b.  -	- indicates the negative square root of 49.
     Since 7^2 = 49, - = -7.

c.  ±	± indicates both square roots of 16.
     Since 4^2 = 16, = 4 and -= -4.

d.  	indicates the positive square root of z^2.
      z may be negative, but  is positive, so = .

Example 2	Find Square Roots with a Calculator
Use a calculator to find each square root to the nearest tenth.
a. 
   
       2nd [] 12 ENTER 3.464101615		Use a calculator.
        ≈ 3.5					Round to the nearest tenth.
  							CHECK  Since (3.5)^2 = 12.25, the
								     answer is reasonable.

b.  -

2nd [] 40 ENTER 6.32455532		Use a calculator.
- ≈ -6.3 					Round to the nearest tenth.
							CHECK   Since (-6)^2 = 36, the            
         			                                                                  answer is reasonable.

Example 3	Estimate Square Roots
Estimate each square root to the nearest whole number.
a. 

•	The first perfect square less than 50 is 49.		= 7
•	The first perfect square greater than 50 is 64.		= 8
•	Plot each square root on a number line.

The square root of 50 is between the whole numbers 7 and 8.  Since 50 is closer to
   49 than 64, the best whole number estimate is 7.

b.  -

•	The first perfect square less than 140 is121.		=11
•	The first perfect square greater than 140 is 144.	=12
•	Plot each square root on a number line.

The negative square root of 140 is between the whole numbers -11 and -12.  Since 140 is closer to 144 than 121, you can expect that - is closer to -12 than -11.

Example 4	Use Square Roots to Solve a Problem
SCIENCE	To estimate how far you can see from a point above the horizon, you can use the formula D = 1.22 ×  where D is the distance in miles and A is the altitude, or height, in feet.  Use this information to determine how far you can see when standing on the top of an office building that is 350 feet high.  Round to the nearest tenth.      ESTIMATE:  1 × = 1 × 19 = 19

D = 1.22 × 			Write the formula.
    = 1.22 × 			Replace A with 350.
    ≈ 22.8262				Evaluate the square root first.  Then multiply.

On a clear day, you can see about 22.8 miles from the top of the office building.