Since you define division in terms of multiplication, you can extend the property for multiplying radical expressions. If the indexes are the same, you can write a quotient of roots as a root of a quotient.
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Take Note Property: Combining Radical Expressions: Quotients
If
Problem 4 Dividing Radical Expressions
What is the simplest form of the quotient?
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Think
Do you need to include absolute value symbols?
No. Both the divisor and dividend already require that x be nonnegative.
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✓ Got It?
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- What is the simplest form of
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Reasoning Can you simplify the expression in Problem 4(a) by first simplifying
- What is the simplest form of
Another way to simplify a radical expression is to rationalize the denominator. You rewrite the expression so that there are no radicals in any denominator and no denominator in any radical.
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions