Adding and Subtracting Radical Expressions When two radical expressions have the same indices and radicands, they are said to be like radicals. Like radicals can be combined (added or subtracted) in much the same way that we combined like terms earlier in this text. Example Simplify by combining like radical terms.

Products and Quotients of Two or More Radical Terms Example Multiply. Using the distributive law In part (c) of the last example, notice that, m – n, is not itself a radical expression. Pairs of radical terms like, are called conjugates.

Rationalize the denominator: Rationalizing Denominators and Numerators (Part 2) The use of conjugates allows us to rationalize denominators or numerators with two terms. Example Rationalize the denominator: Solution Multiplying by clever form of 1 using the conjugate

To rationalize a numerator with more than one term, we use the conjugate of the numerator.

Terms with Differing Indices To multiply or divide radical terms with different indices, like We can convert to exponential notation, use the rules for exponents, and then convert back to radical notation. Example Multiply and, if possible, simplify: Solution Converting to exponential notation Adding exponents Converting to radical notation Simplifying