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Section 7.1

Section 7.1. Nth Roots and Rational Exponents. By : Alex Petrosky Mary Yoder Zack Russo Tyler wickerham. SECTION 7.1. Students will be able to evaluate nth roots of real numbers using radical notation.

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Section 7.1

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  1. Section 7.1 Nth Roots and Rational Exponents By : Alex Petrosky Mary Yoder Zack Russo Tyler wickerham

  2. SECTION 7.1 Students will be able to evaluate nth roots of real numbers using radical notation. Students will be able to evaluate nth roots of real numbers using rational exponent notation.

  3. REAL NTH ROOTS Let n be an integer greater than 1 and be a real number. If n is odd, then a has one real nth root: If n is even a>0, then a has two real nth roots:

  4. REAL NTH ROOTS If n is even and a<0, then a has no real nth roots. If n is even then and a=0, then a has one nth root:

  5. Example 1Finding nth Roots A. n=3, a=-125 Because n=3 is odd, a=-125 has one real cube root. Because (-5) ³ = -125. you can write: or

  6. Example 1Finding nth Roots B. n=4, a=16 Because n=4 is even and a= 16>0, 16 has two real fourth roots. Because 2= 16 and (-2) =16, you can write: Or

  7. Nth Roots A rational exponent does not have to be of the form where n is an integer greater than 1. Other rational numbers such as and can also be used as exponents.

  8. RATIONAL EXPONENTS Let be an Nth root of a, and let m be a positive integer.

  9. Example 2Evaluating expression Using radical notation. Using rational exponent notation. Using radical notation. Using rational exponent notation.

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