Martin-Gay, Developmental Mathematics 1 Warm-Up #6 (Thursday, 9/17)

Martin-Gay, Developmental Mathematics 2 Warm-Up #7 (Friday, 9/18)

Martin-Gay, Developmental Mathematics 3 Homework (Thursday, 9/17) Lesson 1.03_pg 14 Advanced: #1, 2, 9, 10 Regular: #1, #2

Martin-Gay, Developmental Mathematics 4 Homework (Friday, 9/18) Advanced: make sure to have warm-up #4-7 Regular: make sure to have warm-up #4-7 Lesson 1.03_pg 14_#1 and #2

Martin-Gay, Developmental Mathematics 5 The cube root of a real number a Example: Cube Roots

Simplifying Radicals

Martin-Gay, Developmental Mathematics 7 Cube Roots A cube root of any positive number is positive. Examples: A cube root of any negative number is negative – Introduction to Radicals

Martin-Gay, Developmental Mathematics 8 Cube Roots Example

Martin-Gay, Developmental Mathematics 9 If and are real numbers, Product Rule for Radicals

Martin-Gay, Developmental Mathematics 10 Simplify the following radical expressions. No perfect square factor, so the radical is already simplified. Simplifying Radicals Example

Martin-Gay, Developmental Mathematics 11 Simplify the following radical expressions. Simplifying Radicals Example

Martin-Gay, Developmental Mathematics 12 If and are real numbers, Quotient Rule for Radicals

Martin-Gay, Developmental Mathematics 13 Simplify the following radical expressions. Simplifying Radicals Example

Adding and Subtracting Radicals

Martin-Gay, Developmental Mathematics 15 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, Developmental Mathematics 16 What is combining “like terms”? Similarly, we can work with the concept of “like” radicals to combine radicals with the same radicand. Like Radicals

Martin-Gay, Developmental Mathematics 17 Can not simplify Adding and Subtracting Radical Expressions Example

Martin-Gay, Developmental Mathematics 18 Simplify the following radical expression. Example Adding and Subtracting Radical Expressions

Martin-Gay, Developmental Mathematics 19 Simplify the following radical expression. Example Adding and Subtracting Radical Expressions

Martin-Gay, Developmental Mathematics 20 Simplify the following radical expression. Assume that variables represent positive real numbers. Example Adding and Subtracting Radical Expressions

Multiplying and Dividing Radicals

Martin-Gay, Developmental Mathematics 22 If and are real numbers, Multiplying and Dividing Radical Expressions

Martin-Gay, Developmental Mathematics 23 Simplify the following radical expressions. Multiplying and Dividing Radical Expressions Example

Martin-Gay, Developmental Mathematics 24 If we rewrite the expression so that there is no radical in the denominator, it is called rationalizing the denominator. Rationalizing the denominator is the process of eliminating the radical in the denominator. Rationalizing the Denominator

Martin-Gay, Developmental Mathematics 25 Rationalize the denominator. Rationalizing the Denominator Example

Martin-Gay, Developmental Mathematics 26 Many rational quotients have a sum or difference of terms in a denominator, rather than a single radical. need to multiply by the conjugate of the denominator The conjugate uses the same terms, but the opposite operation (+ or  ). Conjugates

Martin-Gay, Developmental Mathematics 27

Martin-Gay, Developmental Mathematics 28 Rationalize the denominator. Rationalizing the Denominator Example