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17: Radical Expressions and Functions

Last updated

Aug 13, 2020
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- 16.E: Review Exercises 2
- 17.1: Prelude to Roots and Radicals

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17.1: Prelude to Roots and Radicals
17.2: Simplify Expressions with Roots
- 17.2E: Exercises
17.3: Simplify Radical Expressions
We will simplify radical expressions in a way similar to how we simplified fractions. A fraction is simplified if there are no common factors in the numerator and denominator. To simplify a fraction, we look for any common factors in the numerator and denominator. A radical expression, ⁿ√ a , is considered simplified if it has no factors of mⁿ. So, to simplify a radical expression, we look for any factors in the radicand that are powers of the index.
- 17.3E: Exercises
17.4: Simplify Rational Exponents
Rational exponents are another way of writing expressions with radicals. When we use rational exponents, we can apply the properties of exponents to simplify expressions.
- 17.4E: Exercises
17.5: Add, Subtract, and Multiply Radical Expressions
Adding radical expressions with the same index and the same radicand is just like adding like terms. We call radicals with the same index and the same radicand like radicals to remind us they work the same as like terms.
- 17.5E: Exercises
17.6: Divide Radical Expressions
We have used the Quotient Property of Radical Expressions to simplify roots of fractions. We will need to use this property ‘in reverse’ to simplify a fraction with radicals. We give the Quotient Property of Radical Expressions again for easy reference. Remember, we assume all variables are greater than or equal to zero so that no absolute value bars re needed.
- 17.6E: Exercises
17.7: Solve Radical Equations
- 17.7E: Exercises
17.8: Use Radicals in Functions
In this section we will extend our previous work with functions to include radicals. If a function is defined by a radical expression, we call it a radical function.
- 17.8E: Exercises
17.9: Use the Complex Number System
- 17.9E: Exercises
17.10: Review Exercises

Thumbnail: The mathematical expression "The (principal) square root of x". Image used with permission (GPL, David Vignoni (original icon); Flamurai (SVG convertion); bayo (color)).

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