Page 149 - Math Course 2 (Book 1)

Radical Expressions

Mo. 5

Lesson 2 Expressions with Unlike Radicands

Example
KEY CONCEPTS:
1. Add and subtract radical expressions.
2. Multiply radical expressions. Simplify 6 27 + 8 12 + 2 75

6 27 + 8 12 + 2 75

2
5
2
=6 3 • 3 + 8 2 • 3 + 2 • 3
MO. 5 - L2a

Radical Expressions: =6 (3 3 ) + 8 (2 3 )+ 2 (5 3 )
Add, Subtract, Multiply = 18 3 + 16 3 + 10 3
= 44 3

Let’s Begin Answer

Expressions with Like Radicands Multiply Radical Expressions

Examples GEOMETRY
Find the area of a rectangle in simplest form with a
10
width of and length of
6 – 2
4
Simplify 6 5 + 2 5 – 5 5
5 3 + 7 5
6 5 + 2 5 – 5 5 = (6 + 2 – 5) 5 To f nd the area of the rectangle, multiply the
Distributive Property measures of the length and width.

= 3 5 5 3 + 7 5
Simplify.

4 6 – 2 10

Answer 3 5

( 4 6 – 2 10 )( 5 3 + 7 5 )
First Outer Inner Last
terms terms terms terms
Simplify 7 2 + 8 11– 4 11 – 6 2
(4 6)(5 3)+(4 6)(7 5)+(–2 10)(5 3)+(–2 10)(7 5)
7 2+ 8 11– 4 11– 6 2
= 20 18 + 28 30 – 10 30 – 14 50 Multiply.
=7 5–6 2 +8 11 –4 11 Commutative Property
2
2
= 20 3 • 2+28 30 –10 30–14 5 • 2 Prime
= (7 – 6) 2 + (8 – 4) 11 Distributive Property factorization
= 60 2 + 28 30 – 10 30 – 70 2 Simplify.
= 2 + 4 11 Simplify.

= 18 30 – 10 2 Combine like
terms.

Answer 2 + 4 11 Answer The area of the rectangle is
18 30 – 10 2 square units.

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