Radicals and Radical Functions

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Presentation transcript:

Radicals and Radical Functions 8.3 Radicals and Radical Functions

Square Roots Opposite of squaring a number is taking the square root of a number. A number b is a square root of a number a if b2 = a. In order to find a square root of a, you need a number that, when squared, equals a.

Radicands _________________is an expression containing a ___________. ____________ is the expression under a radical sign. Note that if the radicand of a square root is a negative number, the radical is NOT a real number.

Principal Square Roots Principal and Negative Square Roots If a is a nonnegative number, then is the principal or nonnegative square root of a is the negative square root of a.

Example Find each square root. a. b. c. d.

Example Find each cube root. a. b. c. d.

nth Roots Other roots can be found, as well. The nth root of a is defined as If the index, n, is even, the root is NOT a real number when a is negative. If the index is odd, the root will be a real number.

Example Find each root. a. b. c.