Intro W13

• Icon Progress Bar/Navigation (built in browser, hidden in app)

        Intro W13

  •  Objectives

    1. The sections for this week are:
       • 9.4 Multiply Square Roots
       • 9.5 Divide Square Roots
       • 9.6 Solve Equations with Square Roots

   

   Intro and Learning Objectives (click on all tabs to see all sections)

  • 9.4

     Learning Outcomes

    In this section, you will:

    • Multiply square roots
    • Use polynomial multiplication to multiply square roots

     Intro

    We have used the Product Property of Square Roots to simplify square roots by removing the perfect square factors. The Product Property of Square Roots says

    \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\)

    We can use the Product Property of Square Roots ‘in reverse’ to multiply square roots.

    \(\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\)

     

    9.5

     Learning Outcomes

    In this section, you will:

    • Divide square roots
    • Rationalize a one-term denominator
    • Rationalize a two-term denominator

     Intro

    We have used the Quotient Property of Square Roots to simplify square roots of fractions. The Quotient Property of Square Roots says

    $$<img\; class="equation\_image"\; title="\backslash sqrt\{\backslash frac\{a\}\{b\}\}=\backslash frac\{\backslash sqrt\{a\}\}\{\backslash sqrt\{b\}\}\backslash :,\backslash :b\backslash ne0"\; src="https://collegeofthedesert.instructure.com/equation\_images/\%255Csqrt\%257B\%255Cfrac\%257Ba\%257D\%257Bb\%257D\%257D\%253D\%255Cfrac\%257B\%255Csqrt\%257Ba\%257D\%257D\%257B\%255Csqrt\%257Bb\%257D\%257D\%255C\%253A\%252C\%255C\%253Ab\%255Cne0?scale=1"\; alt="LaTeX:\; \backslash sqrt\{\backslash frac\{a\}\{b\}\}=\backslash frac\{\backslash sqrt\{a\}\}\{\backslash sqrt\{b\}\}\backslash :,\backslash :b\backslash ne0"\; data-equation-content="\backslash sqrt\{\backslash frac\{a\}\{b\}\}=\backslash frac\{\backslash sqrt\{a\}\}\{\backslash sqrt\{b\}\}\backslash :,\backslash :b\backslash ne0"\; loading="lazy"\; mathjaxified=""><span\; class="math\_equation\_latex"\; style="null">\backslash (\backslash sqrt\{\backslash frac\{a\}\{b\}\}=\backslash frac\{\backslash sqrt\{a\}\}\{\backslash sqrt\{b\}\}\backslash :,\backslash :b\backslash ne0\backslash )</span>,$$

    Sometimes we will need to use the Quotient Property of Square Roots ‘in reverse’ to simplify a fraction with square roots.

    \(\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}},\:\:b\ne0\)

    9.6

     Learning Outcomes

    In this section, you will:

    • Solve radical equations
    • Use square roots in applications

     Intro

    In this section we will solve equations that have the variable in the radicand of a square root. Equations of this type are called radical equations.

    As usual, in solving these equations, what we do to one side of an equation we must do to the other side as well. Since squaring a quantity and taking a square root are ‘opposite’ operations, we will square both sides in order to remove the radical sign and solve for the variable inside.

    But remember that when we write $\sqrt{a}$ we mean the principal square root. So $\sqrt{a}\ge0$ always. When we solve radical equations by squaring both sides we may get an algebraic solution that would make $\sqrt{a}$ negative. This algebraic solution would not be a solution to the original radical equation; it is an extraneous solution. We saw extraneous solutions when we solved rational equations, too.

     Readings

    1. Text: Read the sections from Openstax book Links to an external site. (Links to an external site.)
    2. Videos: Watch all the videos from "Resources W13"

     Assignments

    • Take Notes Week 13         Due Friday night.
      

    Directions

    •  Each section is accompanied by a Handout. Each Handout contains a few definitions, a few "How To" explanations, examples, and "Try It" exercises. Using the structure of the handout you have to write your own notes. Your notes must contain:

    • • Your name
      • The name of the section
      • Definitions and "How To" from the provided handout (this is optional, however, it will be a good idea to have the complete notes)
      • Everywhere there is a "Read Ex nr..." you have to read the example from the ebook and write in your notes : "I read the Ex nr..." . The link for the section in the ebook is provided at the bottom of the page.
      • You have to solve ALL "Try It" exercises.

    After you complete your notes you have to submit them. See Take Notes Methods. 

     

    • Video quizzes Week 13          Due Saturday night 11:59pm.

    Directions

    • To learn the material for this sections, take notes while watching each video and then demonstrate what you learned by doing the exercise below it.

     

    • Homework Week  13              Due Sunday night 11:59pm.
    •  

    Directions

    • There are 3 Practice Homework this week. This are online Homework but you do not have to leave Canvas. Just click on each link, answer the questions, and came back for the next section. There is no partial credit, each question is either 100% good or not. However you have unlimited attempts for each question. A 5% per day penalty applies for Late work if you'll do it until Tuesday night. After that the Homework will be open only for practice.

     

  The due dates for assignments are Friday, Saturday, and Sunday.

  However, you can submit them until Tuesday night next week.

  A 5% per day penalty applies for late work if you'll do it until Tuesday night.