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Mastering Radical Expressions: Square Roots & Higher Order Roots

Understand square roots, cube roots, and higher order roots. Learn about radical expressions and functions with examples. Find domains and simplify expressions with rational exponents. Master evaluating higher order radicals.

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Mastering Radical Expressions: Square Roots & Higher Order Roots

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  1. § 7.2 Radical Expressions and Functions

  2. Definition of Square Root If x is a nonnegative real number, then is the nonnegative (or principal) square root of x; in other words, Index Radical expression 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 principalsquare root. Radical sign Radicand When no number for n appears, 2 is the index.

  3. “Cube root” Example: Find the root of Higher Order Roots • Definition of Higher Order Roots • If x is a nonnegative real number, then is a nonnegative nth root and has the property that • If x is a negative real number, then

  4. Example: Find f(3) for the function and find the domain. The domain is all real numbers x where 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. To find the domain, we know that 3x – 5 must be nonnegative.

  5. Expressions with Rational Exponents If n is a positive integer and x is a nonnegative real number, then Example: Change w3/4 to radical form. Example: Change (3abc)2/5 to radical form.

  6. Evaluating Higher Order Radicals For all real numbers x (including negative real numbers), then Example: Simplify.

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