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Please open Daily Quiz 35.

A scientific calculator may be used on this quiz . You can keep your yellow formula sheets out when you take the quiz. Remember to turn in your answer sheet to the TA when the quiz time is up. . Please open Daily Quiz 35.

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Please open Daily Quiz 35.

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  1. A scientific calculator may be used on this quiz. • You can keep your yellow formula sheets out when you take the quiz. • Remember to turn in your answer sheetto the TA when the quiz time is up. Please open Daily Quiz 35. If you have any time left after finishing the quiz problems, CHECK YOUR ANSWERSbefore you submit the quiz.

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

  3. Section 10.3 Simplifying Radical Expressions

  4. Recall these square root problems from Section 10.1: Examples: (72)½= = 7

  5. What we did in the previous examples was essentially to divide the exponent of each base by 2, which is index of the radical for square roots. But what happens if the radicand ( the expression under the radical) is not a perfect square, i.e. has exponents that are not divisible by 2? Example: How would we simplify Solution: • Think of this as dividing the exponent 7 by the index 2 • Two goes into seven 3 timeswith a remainder of 1

  6. Example Simplify Answer:

  7. Problem from today’s homework:

  8. If we have a radical with an index of 3 or higher, we can use the same process to simplify the radical. Example: How would we simplify Solution: • Divide the exponent 7 by the index 3 • Three goes into seven 2 timeswith a remainder of 1

  9. Example Simplify Answer:

  10. Problem from today’s homework:

  11. If and are real numbers, then Product and Quotient Rules for Radicals: Why is this condition important? No, because square roots of negative numbers are not real numbers.

  12. Example (Assume x and y are ≥ 0) Simplify the following radical expressions. (Assume a > 0 and b ≠ 0)

  13. Problem from today’s homework:

  14. Problem from today’s homework: 5

  15. Example Use the quotient rule to divide, then simplify if possible: Answer:

  16. 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. Example: (x2 + 5x – 1) + (6x2 - 3x + 4) = 7x2 + 2x + 3 • Similarly, we can work with the concept of “like” radicals to combine radicals with the same radicand.

  17. 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.

  18. Example Can not simplify (different indices) Can not simplify (different radicands)

  19. Always simplify radicals FIRST to determine whether there are like radicals to be combined.

  20. Example Simplify the following radical expression.

  21. REMINDER: The assignment on today’s material (HW 41) is due at the start of the next class session. Please open your laptops and work on the homework assignment until the end of the class period. Lab hours in 203: Mondays through Thursdays 8:00 a.m. to 7:30 p.m. Please remember to sign in on the Math 110 clipboard by the front door of the lab

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