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Unit 3: Algebra: Rational Exponents and Square Root Functions

Unit 3: Algebra: Rational Exponents and Square Root Functions. 3.1 – Evaluate n th Roots and Use Rational Exponents . Georgia Performance Standards. MM3A2a Define and understand the properties of n th roots MM3A2b Extend properties of exponents to include rational exponents MM3A3d

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Unit 3: Algebra: Rational Exponents and Square Root Functions

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  1. Unit 3: Algebra: Rational Exponents and Square Root Functions 3.1 – Evaluate nth Roots and Use Rational Exponents

  2. Georgia Performance Standards • MM3A2a • Define and understand the properties of nth roots • MM3A2b • Extend properties of exponents to include rational exponents • MM3A3d • Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology

  3. Vocabulary • For an integer n greater than 1, if bn = a, then b is an nth root of a. • An nth root of a is written as where n is the index of the radical.If n is odd, then a has one real root. If n is even, then a has two real nth roots if a > 0, one real nth root if a = 0, and no real nth roots if a < 0.

  4. Radicals and rational exponents • How can you write the root of an integer using an exponent? An nth root of x is written as where n is the index of the radical. Index Radicand

  5. Radial Review – Think trees

  6. Radial Review

  7. Radial Review • Solve the Following:

  8. Radial Review Solve the Following:. -4 -3 • Solve the Following: • * • * • 2 * 3 • *

  9. Evaluate (a) 95/2 and (b) 27-2/3 Rational Exponent Form 27-2/3== = = • 95/2= (91/2)5= 35= 243

  10. Evaluate (a) 95/2 and (b) 27-2/3 Radical Form 27-2/3== = • 95/2= ()5= 35= 243

  11. Using a calculator • Calculator Steps:

  12. Solve equations using nth roots • Solve the equation: • -2x6 = -1458 • (x+2)5 = 35

  13. Solve equations using nth roots • Solve the equation. Round the result to two decimal places: • x3 + 17 = 132 • 2x5 + 73 = 53 • (x+3)4 = 362

  14. Try the following • Page 112 • 1-6 • 7-9 • 16-20 • 25-33

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