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P3. Radicals and Rational Exponents

P3. Radicals and Rational Exponents. Ch. P3: Radicals and Rational Exponents. SIMPLIFY EVALUATE using order of operations (Ex #1). Definitions. Radical sign Radicand Radical Expression Principal Square root Simplify a square root Conjugates. RULES for Square Roots.

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P3. Radicals and Rational Exponents

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  1. P3.Radicals and Rational Exponents

  2. Ch. P3: Radicals and Rational Exponents SIMPLIFY EVALUATE using order of operations (Ex #1)

  3. Definitions • Radical sign • Radicand • Radical Expression • Principal Square root • Simplify a square root • Conjugates

  4. RULES for Square Roots The Product Rule • If a and b represent nonnegative real number, then The Quotient Rule • If a and b represent nonnegative real numbers and b does not equal 0, then Adding and Subtracting You may only add “like” radicals

  5. Square Roots of Perfect SquaresThe principal square root of a2 is the absolute value of a. In other words, the principal square root of a2 is the positive root! Ex:

  6. Simplify with Product & Quotient rule: To simplify means ______________ Ex#2 a. b. Ex #3 • b.

  7. YOU TRY:

  8. Adding/ Subtracting Like Radicals Ex#4 a. b. Ex #5 a. b.

  9. YOU TRY: a. b. • b.

  10. APPLY: Simplify

  11. Let’s go back to yester-year…. Evaluate the following:

  12. RATIONALIZE THE DENOMINATOR THE TRICK? Evaluate the following:

  13. Rationalize The Denominator Ex #6

  14. Rationalize with Conjugates Ex #7

  15. The End (Day 1)HW: pg. 42 #1-53 odd

  16. Radicals and Rational Exponents (DAY 2)OTHER POWERS

  17. QUESTION OF THE DAY • WHAT RULES DO YOU ALREADY KNOW ABOUT EXPONENETS? (WARM UP RELATED TO THIS) • THEN Discovery activity (next slide) • HOW ARE RADICALS AND RATIONAL EXPONENTS RELATED TO EACH OTHER?

  18. Use your calculator to complete the table below: What do you notice about your answers to the problems in the same row? 2. Is there some pattern that relates the two expressions in each row to one another? Describe the pattern. 3. Given the expression , what expression using a root symbol would yield the same numerical value? 4. Given the expression what expression utilizing a fractional exponent would yield the same numerical value?

  19. Definitions • Rational exponents • Index • Also, if

  20. Simplify Higher Roots Ex #8

  21. YOU TRY:

  22. Combining Cube Roots Ex #9 You try:

  23. Using definition of am/n (Refer back to warm up) Ex #10 Ex #11

  24. Simplifying Expressions with Rational Exponents Ex #12 • (5x1/2)(7x3/4)

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