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Ch. 7.3 Binomial Radical Expression
Binomial Radical Expressions
ALGEBRA 2 LESSON 7-3
Add or subtract if possible.
a. 7
xy + 3
xy
7
xy + 3
xy = (7 + 3)
= 10
b. 2
3
x–2
3
xy
xy
Distributive Property
Add.
5
The radicals are not like radicals. They cannot be combined.
7-3
P. 347 Check understanding #1 A - C
Binomial Radical Expressions
ALGEBRA 2 LESSON 7-3
The rectangular window shown below is made up of three
equilateral triangles and two right triangles. The equilateral triangles
have sides of length 4 feet. What is the perimeter of the window?
The height of an equilateral triangle with side length 4 ft is 2
So the window’s height is 2
3 ft.
The length of the window is 8 ft.
The perimeter is 2(2
3 + 8) ft or 16 + 4
7-3
3 ft.
3 ft.
Binomial Radical Expressions
ALGEBRA 2 LESSON 7-3
3
20 –
45 + 4
Simplify 3
20 –
80 = 3
22 • 5 –
=3•2
=6
45 + 4
32 • 5 + 4
5–3
5–3
5+4•4
5 + 16
= (6 – 3 + 16)
= 19
80.
5
5
7-3
5
42 • 5
5
Factor each radicand.
Simplify each radical.
Multiply.
Use the Distributive Property.
Check understanding p. 375 # 3
Binomial Radical Expressions
ALGEBRA 2 LESSON 7-3
Multiply (2 + 4
(2 + 4
3)(1 – 5
3)(1 – 5
3) = 2 • 1 – 2 • 5
= 2 + (4 – 10)
= –58 – 6
3+4
3 – 60
3
7-3
3).
3•1–4
3•5
3
Use FOIL.
Distributive Property
Check understanding p. 375 # 4
Binomial Radical Expressions
ALGEBRA 2 LESSON 7-3
7)(3 –
Multiply (3 +
(3 +
7)(3 –
7) = 32 – (
7)2
7).
(a + b)(a – b) = a2 – b2
=9–7=2
7-3
Binomial Radical Expressions
ALGEBRA 2 LESSON 7-3
Rationalize the denominator of
2–
3
4+
3
=
=
=
=
2–
3
4+
3
•
2–
3
4+
3
8–2
4–
3
4–
3
•
3–4
42 – (
11 – 6
13
4–
4–
3
4–
3
3+(
3)2
Simplify.
3
7-3
3
4+
3
3 is the conjugate of 4 +
Multiply.
3)2
2–
3.
Homework
Page 376, Exercises: 2 – 42 (EOE)