Nth Root and Rational Exponents Section 7.1
Dec 22, 2015
WHAT YOU WILL LEARN:
1. How to evaluate nth roots of real numbers using both radical notation and rational exponent notation.
2. How to use nth roots to solve real-life problems.
Roots Other than Squares
23 is 8
We can also say the cube root of 8 is 2. (What number times itself 3 times is 8)
This is more commonly written
The number written outside of the radical sign is called the index and tells you what root you are looking for.
3 8
Rational Exponents
16Roots can also be written as rational
exponents. For example: can be rewritten as 16 ½
How do you think you would rewrite the following? 3 64
More About Rational Exponents
2
3
9
Rational exponents do not have to have a numerator of 1. For instance:
• The denominator is the index or root of the number under the radical.
• The numerator is the power that you raise the “answer” to.
“Mathy” Definition
mn a
Let a 1/n be an nth root of a, and let m be a positive integer.
a m/n = (a 1/n)m =
a -m/n = mn
mnnmaaa
1
)(
11/1/
A Lovely Word Problem• The volume for the volume V of a regular
dodecahedron is v = 7.66a3 where a is the length of an edge of the dodecahedron. Find the length of an edge of a regular dodecahedron that has a volume of 30 cubic feet.