Algebra 2 Notes
Algebra 2 Notes Name: ________________
Section 6.6 – Radical Expressions & Radical Exponents
You are probably familiar with finding the square and square root of a number. These two operations are inverses of each other. Similarly, there are roots that correspond to larger powers.
[pic] and [pic] are _________________ roots of [pic] because [pic] and [pic].
[pic] is the _________________ root of [pic] because [pic].
[pic] and [pic] are _________________ roots of 16 because [pic] and [pic].
[pic] is the _________________ roots of [pic] if [pic].
The [pic]th root of a real number [pic] can be written as the radical expression _________________, where [pic] is the _________________ of the radical and [pic] is the _________________. When a number has more than one real root, the radical sign indicates only the _________________, or positive, root.
|Numbers and Types of Real Roots |
|Case |Roots |Example |
|Odd index |1 real root |The real 3rd root of 8 is 2. |
|Even index; positive radicand |2 real roots |The real 4th roots of 16 are [pic]2. |
|Even index; negative radicand |0 real roots |-16 has no real 4th root. |
|Radicand of 0 |1 root of 0 |The 3rd root of 0 is 0. |
Example 1: Find all real roots.
|a. fourth roots of 81 |b. cube roots of -125 |c. square root of –25 |
| | | |
The properties of square roots also apply to [pic]th roots.
|Properties of [pic]th Roots |
|For [pic] and [pic], |
|Words |Numbers |Algebra |
|Product Property of Roots | | |
|The [pic]th root of a product is equal to the product of the|[pic] |[pic] |
|n[pic] roots. | | |
|Quotient Property of Roots | | |
|The [pic]th root of a quotient is equal to the quotient of |[pic] |[pic] |
|the [pic]th root. | | |
Example 2: Simplify each expression. Assume that all variables are positive.
|a. [pic] |b. [pic] |c. [pic] |d. [pic] |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
A ____________________ exponent is an exponent that can be expressed as _______________, where [pic] and [pic] are integers and [pic]. ____________________ expressions can be written by using rational exponents.
|Rational Exponents |
|For any natural number [pic] and integer [pic], |
|Words |Numbers |Algebra |
|The exponent [pic] indicates the [pic]th root. |[pic] |[pic] |
|The exponent [pic] indicated the [pic]th root raised to the | | |
|[pic]th power. |[pic] |[pic] |
Example 3: Write the expression in radical form and then simplify.
|a. [pic] |b. [pic] |c. [pic] |d. [pic] |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
Example 4: Rewrite each expression using rational exponents. Then simplify when possible.
|a. [pic] |b. [pic] |c. [pic] |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
Rational exponents have the same properties as integer exponents. Look back in Section 1.5 in your book if you need to remember…
Example 5: Simplify each expression.
|a. [pic] |b. [pic] |c. [pic] |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- algebra 2 worksheet and answers
- algebra 2 logarithms pdf
- algebra 2 piecewise function worksheet
- algebra 2 absolute value worksheet
- algebra 2 book glencoe pdf
- glencoe algebra 2 textbook pdf
- algebra 2 logarithms worksheet answers
- logarithms algebra 2 practice problems
- algebra 2 equations and inequalities
- algebra 2 inequalities worksheet
- mcdougal littell algebra 2 workbook
- mcdougal littell algebra 2 online textbook