Alg II 6­2 Multiplying and Dividing Radical Expressions ­ End.notebook
January 06, 2017
6-2 Multiplying and Dividing Radical Expressions
You can simplify the product of powers that have the same exponent. Similarly, you can simplify the product of radicals that have the same index.
Ex. 1 Multiply, if possible. Then simplify.
A.
B.
C.
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Alg II 6­2 Multiplying and Dividing Radical Expressions ­ End.notebook
January 06, 2017
Reducing Roots
If the radicand, a, of has a perfect nth power among its factors, you can reduce the radical. If you reduce a radical as much as possible, the radical is in simplest form.
Ex. 2 Simplify. Assume that all variables are positive.
A.
B.
C.
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Alg II 6­2 Multiplying and Dividing Radical Expressions ­ End.notebook
January 06, 2017
Ex. 3 Multiply and simplify. Assume that all variables are positive.
A.
B.
C.
nth Roots of nth Powers
Division is defined in terms of multiplication. If the indexes are the same, you can write a quotient of roots as a root of a quotient.
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Alg II 6­2 Multiplying and Dividing Radical Expressions ­ End.notebook
January 06, 2017
Ex. 4 Divide and simplify. Assume that all variables are positive.
A.
B.
C.
D.
Rationalize the Denominator
Another way to simplify a radical expression is to rationalize the denominator. Rewrite the expression so that there are no radicals in the denominator.
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Alg II 6­2 Multiplying and Dividing Radical Expressions ­ End.notebook
January 06, 2017
Ex. 5 Rationalize the denominator of each expression.
A.
B.
C.
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