5.6 Radical Expressions Objectives: 1.Simplify radical expressions. 2.Add, subtract, multiply and divide radical expressions.

Simplifying Radials Radicals are considered simplified when the following occurs: 1.The index is as small as possible. 2.The radicand contains no factors other than 1 that are the nth powers of an integer or polynomial. 3.The radicand contains no fractions 4.No radicals are in the denominator.

Adding and Subtracting Radicals Like algebraic expressions, radical expressions can only be added or subtracted if the radicands and indices are the same. Sometimes simplifying the radical the radical will create like-radicals.

Product Property of Radicals For any real numbers a and b and any integer n>1 1.If n is even and a and b are both nonnegative, then 2.If n is odd, then Example:

Multiplying Radicals Radicals with different radicands can be multiplied. Multiply coefficients and multiply radicands too. Example:

Quotient Property of Radicals For any real numbers a and b≠0 and any integer n>1, if all roots are defined. Example:

Conjugates Conjugates are binomials that are the same except for the sign between them. Their product will always be a rational number. Example: Forthe conjugate is Multiplying them:

Rationalizing the Denominator One radical in the denominator: 1.Separate radical into two different radicals 2.Simplify radical if possible. 3.Multiply numerator and denominator by radical in denominator or by the radical necessary to get rid of radical. 4.Simplify if necessary. Radical separated by addition/subtraction: 1.Multiply numerator and denominator by conjugate of denominator. 2.Simplify, if necessary.

Examples Simplify. Simplify

More Examples Simplify

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