Lesson 7.3 Binomial Radical Expressions.notebook
February 06, 2012
Section 7.3 Binomial Radical Expressions
Objectives:
• Be able to add and subtract radical
expressions
• Be able to multiply and divide binomial
radical expressions
We know how to add and subtract like variables:
3x2 + 5x2 =
27y ­ 7y =
5x + 3y =
1
Lesson 7.3 Binomial Radical Expressions.notebook
February 06, 2012
Adding and Subtracting Radical Expressions
Like radicals have the same index and the same radicand
√2 √2 √3 √2
∛5 ∛5 √5 ∛5
a) 5√6 + √6 = e) 2√3 + 3√2 =
b) 3√x ­ 5√x = f) 5√7 ­ 7√7 =
c) 7∛x2 ­ 2∛x2 = g) 10√2 + 5∛2 =
d) 2√3 + 4√2 = h) 3∜y + 5∜y =
2
Lesson 7.3 Binomial Radical Expressions.notebook
February 06, 2012
Simplify before adding or subtracting:
√75x + 2√48x ­ 5√3x
Simplify:
a) 5√12y + 2√3y =
c) 14√20 -3√125 =
b) √27 +√75 ­√12 =
d) ∛54 +∛16 =
3
Lesson 7.3 Binomial Radical Expressions.notebook
February 06, 2012
Multiplying binomial radical expressions
(3 + 2√5)(2 + 4√5) =
(5 +√3 )(2 - 3√3 )
(3 + √5 )(4 + √5 )
(2 + √3 )(2 - √3 )
4
Lesson 7.3 Binomial Radical Expressions.notebook
February 06, 2012
Conjugates are binomial expressions that
differ only in the sign of the second term:
5 + √2 5 ­ √2
3 ­ 5∛4 3 + 5∛4
2 + √xy
5 - √3
2 - √xy
5 + √3
What happens when we multiply conjugates?
(2 + √3)(2 ­ √3) =
(3√2 + 9)(3√2 ­ 9) =
5
Lesson 7.3 Binomial Radical Expressions.notebook
February 06, 2012
Now we can rationalize binomial radical
denominators
6 + √5
1 ­ √5
5
2 + √7
4 + √2
1 ­ √2
2 ­ √3
4 + √3
6