College Algebra: Section 1.2c (Packet #5)
By the end of the section, you should be able to:
- Identify the parts of a radical.
- Simplify radical expressions.
- Combine radical expressions.
Definitions:
- Radical: The inverse operation to exponents
- Index: The number outside of the radical sign, shows the power of the root that is taken.
- Radicand: The number inside the radical sign.
- Rationalizing the denominator: A technique that removes the radical from the denominator of a rational expression.
Rules of / Defining Radicals
Simplifying Radicals:
A radical expression is in simplified form when:
A radical expression is in simplified form when:
- The radicand contains no factor with an exponent greater than or equal to the index of the radical.
- The radicand contains no fractions.
- The denominator, if there is one, contains no radical.
- The greatest common factor of the index and any exponent occurring in the radicand is 1. That is, the index and any exponent in the radicand have no common factor other than 1.
Simplifying Radical Expression Examples
🎥Examples 1&2
🎥Examples 1&2
Things to remember about simplifying radicals:
|
Things to remember about rationalizing the denominator:
- Multiply the bottom term by an expression so that product sets the radicand’s power is equal to the index
- If more than one term use the conjugate
- Conjugates look like the same exact expression only with the opposite sign between the terms
If you had any problems with the example videos on this page, or have any comments to make them better, please click the button below.