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§ 7.2

§ 7.2. Radical Expressions and Functions. 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.

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§ 7.2

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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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