University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

243

Pages:

4
Author:

Jace Leach

5.1 nth Roots and Rational Exponents A. Vocabulary & Concepts Rational: Can be written as a ratio (fraction) Radical: √a "nth root of a" e.g., √16 = 4 The 4th root of 16 e.g., ∛8 = 2 The 3rd root of 8 nth root: b^n = a, b is the nth root of a. a^(m/n) = (ⁿ√a)^m = ⁿ√(a^m) n is called the index a^(m/n) = (a^(1/n))^m = (ⁿ√a)^m ⁿ√a = a^(1/n) ⁿ√0 = 0 The nth root of 0 equals 0 Real nth roots of a: If n is even: a < 0: No real nth roots a = 0: One real nth root 0 a > 0: Two real nth roots (positive and negative) If n is odd: a < 0: One real nth root a = 0: One real nth root 0 a > 0: One real nth root 5.1 nth Roots and Rational Exponents A. Vocabulary & Concepts Rational: Can be written as a ratio (fraction) Radical: √a "nth root of a" e.g., √16 = 4 The 4th root of 16 e.g., ∛8 = 2 The 3rd root of 8 nth root: b^n = a, b is the nth root of a. a^(m/n) = (ⁿ√a)^m = ⁿ√(a^m) n is called the index a^(m/n) = (a^(1/n))^m = (ⁿ√a)^m ⁿ√a = a^(1/n) ⁿ√0 = 0 The nth root of 0 equals 0 Real nth roots of a: If n is even: a < 0: No real nth roots a = 0: One real nth root 0 a > 0: Two real nth roots (positive and negative) If n is odd: a < 0: One real nth root a = 0: One real nth root 0 a > 0: One real nth root 2. Evaluate each expression a. 16^(3/2) = (√16)^3 = (4)^3 = 64 b. 32^(-3/5) = 1 / 32^(3/5) = 1 / (⁵√32)^3 = 1 / (2)^3 = 1/8 c. 64^(4/3) = (∛64)^4 = (4)^4 = 256 d. 16^(-5/4) = 1 / 16^(5/4) = 1 / (⁴√16)^5 = 1 / (2)^5 = 1/32 3. Evaluate using a calculator. Round your answer to two decimal places. a. 9^(4/5) = 5.91 Calculator buttons: 9, 2nd, √x, 4, =, x^y, 5, = b. 12^(3/8) = 2.54 Calculator buttons: 12, 2nd, √x, 8, =, x^y, 3, = c. (√7)^3 = 14.30 Calculator buttons: 7, 2nd, √x, =, x^y, 3, = d. 6^(2/5) = 2.05 Calculator buttons: 6, 2nd, √x, 5, =, x^y, 2, = e. 64^(-2/3) = 0.06 64^(-2/3) = 1 / 64^(2/3) = 1 / (∛64)^2 = 1 / (4)^2 = 1/16 = 0.06