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Understanding the Relationship between Nth Roots and Rational Exponents

Explore the connection between nth roots and rational exponents. Learn to evaluate expressions, solve equations, and simplify radicals. Homework included.

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Understanding the Relationship between Nth Roots and Rational Exponents

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  1. 1. √121 WARM UP Evaluate without using a calculator. 2. 5–2 Evaluate without using a calculator. 3. Solve (x + 7)2 = 24. Write answers with radicals in simplest form.

  2. RationalExponents and nth roots EQ: What is the relationship between nth roots and rational exponents? Assessment: Students will write a summary about the relationship between nth roots and rational exponents.

  3. Key Terms • nth root of a – __________________________________________________________________________ • Index of a radical – __________________________________________________________________________ For an integer n greater than 1, if bn = a, then the nth root of a is equal to b An nth root of a is written as , where n is the index of a radical.

  4. Key Concept

  5. Example 1 Find the indicated real nth root(s) of a. a. n = 3, a = –216 b. n = 4, a = 81

  6. Key Concept

  7. Example 2 Evaluate (a) 163/2 and (b)32–3/5. Rational Exponent Form Radical Form

  8. Keystrokes Expression Display 9 1 5 7 3 4 12 3 8 7  c. ( 4 )3 = 73/4 Example 3 Approximate roots with a calculator a. 91/5 1.551845574 b. 123/8 2.539176951 4.303517071

  9. b. (x – 3)4 = 21 a. 4x5 = 128 Example 4 Solve the equation.

  10. 4. 5. ( x + 5 )4 = 16 3x2 = 108 You Try It! Find the indicated real nth root(s) of a. 1. n = 6, a = 64 Evaluate expressions without using a calculator. 2.45/2 3. 9–1/2 Solve the equation.

  11. HOMEWORK Textbook – Pg. 417-418 15,19, 24,25,27,31,33,51-53 • Write your Summary to the Essential Question • What is the relationship between nth roots and rational exponents?

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