Lesson 7–5

Example 1  Simplify Expressions
Simplify. 

a. 			
	= 	Factor into squares where possible.	
	= 	Product Property of Radicals	
	= 5a2x2 	Simplify.	

b. 		c. 		
 =  	Quotient Property	 =  	Quotient Property	
 =  	Factor into squares.	 =  •  	Rationalize the
denominator.	
 =  	Product Property	 =  	Product Property	
 =  	 = d6, 
 = n4	 =  	Multiply.	
 =  •   	Rationalize the denominator.	 =  	 = 2m	
 = 		   = n			

Example 2  Multiply Radicals
Simplify 2 • 5.

2 • 5	= 2 • 5 • 	Product Property of Radicals	
	= 10 • 	Factor into squares where possible.	
	= 10 •  •  •  •  • 	Product Property of Radicals	
	= 10 • 36 • a2 • b •  •  or 360a2b 	Multiply.	

Example 3  Add and Subtract Radicals
Simplify –4 + 5 – 2
–4 + 5 – 2		
= -4 + 5 – 2	Factor using squares.	
= -4 •  + 5 •  – 2 • 	Product Property	
= -4 • 3 •  + 5 • 5 •  – 2 • 7 • 	 = 3,  = 5,  = 7	
= -12 + 25 – 14	Multiply.	
= -	Combine like radicals.	

Example 4  Multiply Radicals
Simplify.
a. (2 – )(3 – 5)
	             F                      O                      I                            L	
(2 – )(3 – 5)	= 2 • 3 +  2 • (–5) + (–) • (3) + (–) • (–5)	
	= 6 – 10 – 3 + 5     Product Property	
	= 6 – 10 – 21 + 5           3 = 3  7 = 21	

b. (4 – 3)(4 + 3)

(4 – 3)(4 + 3)		
= 4 • 4 + 4( 3) + (– 3)(4) + (– 3)( 3)	FOIL	
= 16  + 12  – 12  – 9 	Multiply.	
= 80 – 18	 = 5,  = 2	
= 62	Subtract.	

Example 5  Use a Conjugate to Rationalize a Denominator
Simplify .
	=  • 	Multiply by  because 2 –  is the conjugate of 2 + .	
	= 	Distributive Property for the numerator
FOIL for the denominator	
	= 	Multiply.	
	= 	Combine like terms.	
	= –2 + 	Multiply numerator and denominator by –1.