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All Math 110 finals will be given in your regular classroom.

Make sure you know the day and time of the final exam for this section of Math 110: Day: ______ , Date_____ Time: ______ to _______. All Math 110 finals will be given in your regular classroom.

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All Math 110 finals will be given in your regular classroom.

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  1. Make sure you know the day and time of the final exam for this section of Math 110:Day: ______ , Date_____Time: ______ to _______ All Math 110 finals will be given in your regular classroom. Final exam schedules for all sections are posted on the bulletin board and in your course syllabus.

  2. Math TLC Open Lab Hours: Room 203 Jarvis Hall Science Wing Regular hours (M-Th 8:00-6:30, closed Friday) Finals Week Open Lab Hours: Starting at 10 a.m. on Study Day (Wed.) and 8 a.m. on Final Exam days See schedule posted in the classroom and in the open lab and online at http://www.uwstout.edu/mathtlc

  3. Questions on 7.4B HW?

  4. Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note-taking materials.

  5. Section 7.5 • Many times it is helpful to rewrite a radical quotient with the radical confined to ONLY the numerator. • Remember that numbers such as are called irrational numbers. • If we rewrite a radical quotient so that there is no radical in the denominator, it is called rationalizing the denominator. • This process involves multiplying the quotient by a form of 1 that will eliminate the radical in the denominator.

  6. Examples: Rationalize the denominator.

  7. Problem from today’s homework:

  8. Problem from today’s homework:

  9. Problem from today’s homework:

  10. Many rational quotients have a sum or difference of two square root terms in a denominator, rather than a single radical term. • In that case, we need to multiply by the conjugate of the denominator. • The conjugate uses the same two terms, but the opposite operation (+ or -). • When you multiply (“FOIL”) a two-term radical expression by its conjugate, the middle terms of the product (those containing radicals) will cancel out. • Since the radical (irrational) terms are now gone, only rational numbers are left in the denominator.

  11. Example Rationalize the denominator of Notice that there are no radical terms left in the denominator after the conjugates are multiplied and like terms are combined.

  12. Problem from today’s homework:

  13. Problem from today’s homework:

  14. Problem from today’s homework:

  15. Problem from today’s homework:

  16. Problem from today’s homework:

  17. Example How would you start this problem? First, write it as the quotient of two separate cube roots: Now figure out what to multiply the 5 by to make it a perfect cube: 5 = 51, so 51∙52 = 53 Rationalizing denominators involving a cube root:

  18. Problem from today’s homework:

  19. Problem from today’s homework:

  20. Problem from today’s homework:

  21. Reminders: • The assignment for section 7.5 that we’re covering today is due at the start of class on Monday. • Monday we’ll be reviewing for Test 4, and TEST 4 is on TUESDAY, so plan to start working on Practice Test 4 over the weekend – don’t leave it till Monday night!

  22. You may now OPEN your LAPTOPS and begin working on the homework assignment.

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