7 3 Simplifying Radical Expressions MartinGay Intermediate Algebra

§ 7. 3 Simplifying Radical Expressions Martin-Gay, Intermediate Algebra, 5 ed 1

Product Rule for Radicals If and are real numbers, then Martin-Gay, Intermediate Algebra, 5 ed 2

Simplifying Radicals Example: Simplify the following radical expressions. No perfect square factor, so the radical is already simplified. Martin-Gay, Intermediate Algebra, 5 ed 3

Simplifying Radicals Example: Simplify the following radical expressions. Martin-Gay, Intermediate Algebra, 5 ed 4

Quotient Rule Radicals Quotient Rule for Radicals If and are real numbers, Martin-Gay, Intermediate Algebra, 5 ed 5

Simplifying Radicals Example: Simplify the following radical expressions. Martin-Gay, Intermediate Algebra, 5 ed 6

The Distance Formula The distance d between two points (x 1, y 1) and (x 2, y 2) is given by Martin-Gay, Intermediate Algebra, 5 ed 7

The Distance Formula Example: Find the distance between ( 5, 8) and ( 2, 2). Martin-Gay, Intermediate Algebra, 5 ed 8

The Midpoint Formula The midpoint of the line segment whose endpoints are (x 1, y 1) and (x 2, y 2) is the point with coordinates Martin-Gay, Intermediate Algebra, 5 ed 9

The Midpoint Formula Example: Find the midpoint of the line segment that joins points P( 5, 8) and P( 2, 2). Martin-Gay, Intermediate Algebra, 5 ed 10

§ 7. 4 Adding, Subtracting, and Multiplying Radical Expressions Martin-Gay, Intermediate Algebra, 5 ed 11

Sums and Differences Rules in the previous section allowed us to split radicals that had a radicand which was a product or a quotient. We can NOT split sums or differences. Martin-Gay, Intermediate Algebra, 5 ed 12

Like Radicals In previous chapters, we’ve discussed the concept of “like” terms. These are terms with the same variables raised to the same powers. They can be combined through addition and subtraction. Similarly, we can work with the concept of “like” radicals to combine radicals with the same radicand. Like radicals are radicals with the same index and the same radicand. Like radicals can also be combined with addition or subtraction by using the distributive property. Martin-Gay, Intermediate Algebra, 5 ed 13

Adding and Subtracting Radical Expressions Example: Can not simplify Martin-Gay, Intermediate Algebra, 5 ed 14

Adding and Subtracting Radical Expressions Example: Simplify the following radical expression. Martin-Gay, Intermediate Algebra, 5 ed 15

Adding and Subtracting Radical Expressions Example: Simplify the following radical expression. Martin-Gay, Intermediate Algebra, 5 ed 16

Adding and Subtracting Radical Expressions Example: Simplify the following radical expression. Assume that variables represent positive real numbers. Martin-Gay, Intermediate Algebra, 5 ed 17

Homework t 7. 3 #’s 5 -67 odd Martin-Gay, Intermediate Algebra, 5 ed 18

Multiplying and Dividing Radical Expressions If and are real numbers, Martin-Gay, Intermediate Algebra, 5 ed 19

Multiplying and Dividing Radical Expressions Example: Simplify the following radical expressions. Martin-Gay, Intermediate Algebra, 5 ed 20

Martin-Gay, Intermediate Algebra, 5 ed 23