-
Home
- Algebra and trigonometry
- Prerequisites
- Radicals and rational exponents
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
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Omeprazole
Cimetidine / Tagament
For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
how does the stomach protect itself from the damaging effects of HCl
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
function of digestive
Ali
what is the normal body temperature
please why 37 degree selcius normal temperature
Mark
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
how does Lysin attack pathogens
Diya
I information on anatomy position and digestive system and there enzyme
anatomy of the female external genitalia
Got questions? Join the online conversation and get instant answers!
Source:
OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.