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§ 7.2 Radical Expressions and Functions

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Tobey & Slater, Intermediate Algebra, 5e - Slide #2 Square Roots The square root of a number is a value that when multiplied by itself is equal to the original number. The positive square root is called the principal square root. Definition of Square Root If x is a nonnegative real number, then is the nonnegative (or principal) square root of x; in other words, Radical sign Radicand Radical expression Index When no number for n appears, 2 is the index.

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Tobey & Slater, Intermediate Algebra, 5e - Slide #3 Higher Order Roots Definition of Higher Order Roots 1.If x is a nonnegative real number, then is a nonnegative nth root and has the property that 2.If x is a negative real number, then Example: Find the root of “Cube root”

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Tobey & Slater, Intermediate Algebra, 5e - Slide #4 Square Root Functions The square root function f(x) has a domain of all real numbers x that are greater than or equal to 0. Example: Find f( 3) for the function and find the domain. To find the domain, we know that 3x – 5 must be nonnegative. The domain is all real numbers x where

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Tobey & Slater, Intermediate Algebra, 5e - Slide #5 Expressions with Rational Exponents If n is a positive integer and x is a nonnegative real number, then Example: Change w 3/4 to radical form. Example: Change (3abc) 2/5 to radical form.

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Tobey & Slater, Intermediate Algebra, 5e - Slide #6 Evaluating Higher Order Radicals For all real numbers x (including negative real numbers), then Example: Simplify.

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