6-3: Binomial Radical Expressions

Combining Radical Expressions

6-3: Binomial Radical Expressions
Combine radicals which have same index and
radicands.
Algebra 2
Combining Radical Expressions: Sums and Differences
Use the Distributive Property to add or subtract like radicals:
a n x  b n x  a  b n x
2 5 7 5 3 5
 2  7  3
a n x  b n x  a  b n x
34 7  4 7  2 4 7
34 7  7
3 1  2 4 7  4 4 7
5 6 5
Different Index;
Can’t Combine
Complete Got It? #1 p.375
a. Can't combine
Simplifying Before Combining

c. 2 5 3 x 2
b. 7 x xy
Multiplying Binomial Radical Expressions
Try to simplify to see if have like radicals


What is the simplest form of the expression?
28  175  63  2 7  5 7  3 7
Multiply in way similar to binomial expressions
which don’t contain radicals.
Use the Distributive Property
What is the product of the radical expression?
1  2 7  4  3 7 
  2  5  3 7
 1 4 1 3 7  4 2 7  2 7 3 7
 4  3 7  8 7  6 49
0 7 0
 4  5 7  42
 38  5 7
Complete Got It? #3 p.376
Rationalizing a Denominator Containing
Radical Expressions
Multiplying Binomial Radical Expressions

46  16 5
Complete Got It? #4 p.376
63 2
Conjugates
◦ The product of two conjugates is a rational
number.

Multiply both numerator and denominator by
the conjugate of the denominator.
Write the expression with a rationalized denominator.
What is the product of the radical expression?
5  3 2 5  3 2 
 5 55 3 2 5 3 2 3 2 3 2
 25  15 2  15 2  9 4
 25  0  18
7
Complete Got It? #5 p.377
a. 24
b. 1
11
6 3


11 6  3
6 3

6 3
6 3 6 3




66  11 3
36  9

66  11 3 6  3

33
3
Complete Got It? #6 p.377 a.  21  35
b.
12 x  4 x 6
3
1
Homework: p.378 #11-35 odd, 62-64
2

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