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Any questions on the Section 7.4 homework?

Any questions on the Section 7.4 homework? . Now please CLOSE YOUR LAPTOPS and turn off and put away your cell phones. Sample Problems Page Link (Dr. Bruce Johnston ). Section 7.5.

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Any questions on the Section 7.4 homework?

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  1. Any questions on the Section 7.4 homework?

  2. Now please CLOSE YOUR LAPTOPS and turn off and put away your cell phones. Sample Problems Page Link (Dr. Bruce Johnston)

  3. 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.

  4. Examples: Rationalize the denominator.

  5. Problem from today’s homework:

  6. Problem from today’s homework:

  7. Problem from today’s homework:

  8. 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.

  9. 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.

  10. Problem from today’s homework:

  11. Problem from today’s homework:

  12. Problem from today’s homework:

  13. Problem from today’s homework:

  14. Problem from today’s homework:

  15. 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 roots:

  16. Problem from today’s homework:

  17. Problem from today’s homework:

  18. Problem from today’s homework:

  19. Reminders: • The assignment for section 7.5 that we’re covering today is due at the start of next class session. • At the next class session we’ll be reviewing for Test 4, so it will help if you have at least taken a look at the Practice Test before the start of the next class.

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

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