6.5 Division of Radical Expressions

Rationalize the denominator of a radical expression having one term in the denominator. An equivalent expression without a radical in the denominator provides a standard notation for expressing results. The procedure for finding such an expression is called rationalizing the denominator. Carry this out by multiplying by 1.

1) Rationalize the denominator

2) Rationalize the denominator

More practice 3) 4) 5) Answers: 3) 4) 5)

More practice 6) 7) 8)

Rationalize the denominator of a radical expression having two terms in the denominator. are called conjugates. The product of such a pair of conjugates has no radicals in it. When we want to rationalize a denominator that has two terms and one or more of them involves a square-root radical, multiply by 1 using the conjugate of the denominator to write a symbol for 1.

Rationalize Denominator: eliminate the radical terms in the denominator 1)

Rationalize Denominator: eliminate the radical terms in the denominator 2) 3)

4)

Terms with different indices: convert to exponential notation