Algebra II
Chapter 7
7.3 Binomial Radical Expressions

Objective/ Big Idea
 To add and subtract radical expressions
To multiply and divide binomial radical expressions
Adding and Subtracting Radical Expressions
a. 5 3 x  3 3 x
b. 4 2  5 3
Radical expressions have to have what in common to add or subtract?
Try these…
a. 2 7  3 7
b. 7 4 5  2 3 5
Simplifying Before Adding or Subtracting
6 18  4 8  3 72
Try this one…
50  3 32  5 18
c. 4 xy  5 xy
Multiplying and Dividing Binomial Radical Expressions
(Multiply radical expressions that are in the form of binomials by
FOIL/Distribution)
Multiplying Binomial Radical Expressions
(3  2 5)(2  4 5)
Try this…
( 2  3)2
What is a conjugate?
Find the conjugate of 2  3
Multiply Conjugates
(2  3)(2  3)
What happened when you multiplied radical conjugates??
Find the conjugate of the radical below and then multiply the radical by its
conjugate,
( 5  2)
Rationalizing Binomial Radical Denominators
How do you rationalize a denominator?
What about the denominator of a binomial?
3 5
1 5
Try this one…
6  15
4  15
Name
Class
Date
Practice 7-3
Binomial Radical Expressions
Multiply each pair of conjugates.
1. Q 3"2 2 9 R Q 3"2 1 9 R
2. Q 1 2 "7 R Q 1 1 "7 R
3. Q5"3 1 "2RQ5"3 2 "2R
Add or subtract if possible.
5. 5"2 1 2"3
3
6. 3"7 2 7"
x
Rationalize each denominator. Simplify the answer.
5
2
8.
9.
2"3 2 4
2 1 "3
10.
12. 3"32 1 2"50
3
3
14. "
81 2 3"
3
Simplify.
13. "200 2 "72
3
3
7. 14"
xy 2 3"
xy
1 1 "5
1 2 "5
11.
2 1 "12
5 2 "12
4
4
15. 2"
48 1 3"
243
Multiply.
16. Q 1 2 "5 R Q 2 1 "5 R
17. Q 1 1 4"10 R Q 2 2 "10 R
18. Q 1 2 3"7 R Q 4 2 3"7 R
19. Q 4 2 2"3 R 2
20. Q "2 1 "7 R 2
21. Q 2"3 1 3"2 R 2
All rights reserved.
4. 9"3 1 2"3
22. "28 1 4"63 2 2"7
23. 6"40 2 2"90 1 3"160
24. 3"12 1 7"75 2 "54
3
3
3
81 1 2"
72 2 3"
24
25. 4"
26. 3"225x 1 5"144x
27. 6"45y2 1 4"20y2
28. Q 3!y 2 "5 R Q 2!y 1 5"5 R
29. Q "x 2 "3 R Q "x 1 "3 R
30.
3 2 "10
"5 2 "2
31. 2 1 "14
"7 1 "2
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Simplify. Rationalize all denominators. Assume that all variables are positive.
3
32. 2 13 "x
"x
300 ft
300 3 ft
600 ft
sidewalk
33. A park in the shape of a triangle has a sidewalk dividing it into
two parts.
300 6 ft
300 3 ft
a. If a man walks around the perimeter of the park, how far will
he walk?
b. What is the area of the park?
4
Lesson 7-3 Practice
Algebra 2 Chapter 7