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.
Relationship between Nth Roots and Rational Exponents
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Presentation Transcript
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.
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.
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.
Example 1 Find the indicated real nth root(s) of a. a. n = 3, a = –216 b. n = 4, a = 81
Example 2 Evaluate (a) 163/2 and (b)32–3/5. Rational Exponent Form Radical Form
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
b. (x – 3)4 = 21 a. 4x5 = 128 Example 4 Solve the equation.
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.
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?
