operations with Radicals, algebra homework help

1. Write a sum of three radicals that contains two like terms. Explain how you would combine the terms. Defend your answer.
2. Refer to the information given on page 428 to explain how radical expressions relate to the Mona Lisa. Use the properties in this lesson to explain how you could rewrite the radical expression

7-5
Operations with
Radical Expressions
Main Ideas
• Simplify radical
expressions
• Add, subtract,
multiply, and divide
radical expressions
New Vocabulary
rationalizing the
denominator
like radical expressions
conjugates
GET READY for the Lesson
Golden rectangles have been used by
artists and architects to create beautiful
designs. For example, if you draw a
rectangle around the Mona Lisa’s face,
the resulting quadrilateral is the golden
rectangle. The ratio of the lengths of the
sides of a golden rectangle is?
V5-1
In this lesson, you will learn how to
simplify radical expressions like
V5-1
2
Simplify Radicals The properties you have used to simplify radical
expressions involving square roots also hold true for expressions
involving nth roots.
KEY CONCEPT
Properties of Radicals
For any real numbers a and b and any integer n > 1, the following
properties hold true.
Property
Words
Examples
Product 1. If n is even and a and bare V2.78 = V16, or 4, and
Property both nonnegative, then
V3. V9 = V27, or 3
Vab = VaVb, and
2. If n is odd, then
Vab = VaVb.