-
Home
- College algebra
- Prerequisites
- Radicals and rational expressions
Simplifying rational exponents
Simplify:
-
-
-
-
Got questions? Get instant answers now! Got questions? Get instant answers now!
Key concepts
- The principal square root of a number
is the nonnegative number that when multiplied by itself equals
See
[link] .
- If
and
are nonnegative, the square root of the product
is equal to the product of the square roots of
and
See
[link] and
[link] .
- If
and
are nonnegative, the square root of the quotient
is equal to the quotient of the square roots of
and
See
[link] and
[link] .
- We can add and subtract radical expressions if they have the same radicand and the same index. See
[link] and
[link] .
- Radical expressions written in simplest form do not contain a radical in the denominator. To eliminate the square root radical from the denominator, multiply both the numerator and the denominator by the conjugate of the denominator. See
[link] and
[link] .
- The principal
n th root of
is the number with the same sign as
that when raised to the
n th power equals
These roots have the same properties as square roots.
See
[link] .
- Radicals can be rewritten as rational exponents and rational exponents can be rewritten as radicals. See
[link] and
[link] .
- The properties of exponents apply to rational exponents. See
[link] .
Section exercises
Verbal
What does it mean when a radical does not have an index? Is the expression equal to the radicand? Explain.
When there is no index, it is assumed to be 2 or the square root. The expression would only be equal to the radicand if the index were 1.
Got questions? Get instant answers now!
Numeric
For the following exercises, simplify each expression.
Algebraic
For the following exercises, simplify each expression.
Real-world applications
A guy wire for a suspension bridge runs from the ground diagonally to the top of the closest pylon to make a triangle. We can use the Pythagorean Theorem to find the length of guy wire needed. The square of the distance between the wire on the ground and the pylon on the ground is 90,000 feet. The square of the height of the pylon is 160,000 feet. So the length of the guy wire can be found by evaluating
What is the length of the guy wire?
Got questions? Get instant answers now!
Extensions
For the following exercises, simplify each expression.
Questions & Answers
how did the oxygen help a human being
how did the nutrition help the plants
Biology is a branch of Natural science which deals/About living Organism.
evolutionary history and relationship of an organism or group of organisms
AI-Robot
cell is the smallest unit of the humanity biologically
Abraham
HOW CAN MAN ORGAN FUNCTION
the diagram of the digestive system
allimentary cannel
Ogenrwot
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
Genetics is the study of heredity
Misack
how does twins formed?
Misack
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
list any five characteristics of the blood cells
Shaker
Got questions? Join the online conversation and get instant answers!
Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.