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5.6 Radical Expressions

5.6 Radical Expressions. Objectives: Simplify radical expressions. 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.

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5.6 Radical Expressions

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

  2. 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.

  3. 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.

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

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

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

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

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

  9. Simplify. Simplify Examples

  10. Simplify Simplify More Examples

  11. Homeworkpage 254-25516-52 even

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