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nth Roots and Rational Exponents

nth Roots and Rational Exponents. Lesson 7.1 Goal: Evaluate nth roots of real numbers. Warm-up. 1. If an object travels at five feet per second, how many feet does it travel in one hour? 30 B. 300 C. 720 D. 1800 E. 18000

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nth Roots and Rational Exponents

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  1. nth Roots and Rational Exponents Lesson 7.1 Goal: Evaluate nth roots of real numbers

  2. Warm-up 1. If an object travels at five feet per second, how many feet does it travel in one hour? 30 B. 300 C. 720 D. 1800 E. 18000 2. In a class of 78 students 41 are taking French, 22 are taking German and 9 students are taking both French and German. How many students are not enrolled in either course? A. 6 B. 15 C. 24 D. 33 E. 54 3. What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive? A. 90 B. 95 C. 100 D. 105 E. 110

  3. nth Roots b is the square root of a if b is the cube root of a if b is the fourth root of a if b is the nth root of a if The nth root of a can be written as where a is a real number and n is the index of the radical. refers to the positive nth root of a. refers to the negative nth root of a.

  4. Number of Real nth Roots Let n be an integer greater than 1, and let a be a real number. If n is odd and a is any real number, then n has 1 real root! n a Examples

  5. Number of Real nth Roots Let n be an integer greater than 1, and let a be a real number. If n is even and a is any positive real number, then n has 2 real roots! Examples

  6. Number of Real nth Roots Let n be an integer greater than 1, and let a be a real number. If n is even and a is zero, then n has 1 real root! Examples

  7. Number of Real nth Roots Let n be an integer greater than 1, and let a be a real number. If n is even and a is any negative real number, then n has NO real root! Examples

  8. Number of Real nth Roots Number of Real nth Roots Let n be an integer greater than 1, and let a be a real number.

  9. Example 1: Solve.

  10. Rational Exponents: You do not have to use a radical to write an nth root of a. You can write an nth root of a using a fraction as an exponent. The denominator of each rational exponent is equal to the index of the radical.

  11. Example 2: Evaluate. Does not exist.

  12. Rational Exponents: Rational Exponents You can also use a fraction as an exponent to write a combination of a power and an nth root.

  13. Example 3: Rewrite using exponents.

  14. Example 4: Rewrite using radicals.

  15. Example 5: Evaluate without using a calculator.

  16. Assignment Worksheet 7.1

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