Section 10.3 – 10.4 Multiplying and Dividing Radical Expressions

Questions Q: True or False?  Product /Quotient Rule for Radicals TrueFalse TrueFalse TrueFalse TrueFalse

Product and Quotient Rules 1 ) The power of each factor in the radical is less than the index 2) The radicand contains no fractions or negative numbers 3) No radical appears in the denominator. where a, b are non-negative numbers A radical expression is in simplified form if

Examples Simplify the following expressions

Solution Divide and, if possible, simplify. Because the indices match, we can divide the radicands. Example

Solution continued

Rationalizing Denominators or Numerators With One Term When a radical expression appears in a denominator, it can be useful to find an equivalent expression in which the denominator no longer contains a radical. The procedure for finding such an expression is called rationalizing the denominator.

Solution Rationalize each denominator. Multiplying by 1 Example

Solution

Property of radicals when n is odd when n is even

Evaluate the radical expressions