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- Elementary algebra
- Roots, radicals, and square root
- Summary of key concepts
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
The distinction between the principal square root of the number x and the secondary square root of the number x is made by explanation and by example. The simplification of the radical expressions that both involve and do not involve fractions is shown in many detailed examples; this is followed by an explanation of how and why radicals are eliminated from the denominator of a radical expression. Real-life applications of radical equations have been included, such as problems involving daily output, daily sales, electronic resonance frequency, and kinetic energy.This module presents a summary of the key concepts of the chapter "Roots, Radicals, and Square Root Equations".
Summary of key concepts
Square root (
[link] )
The square root of a positive number
is a number such that when it is squared, the number
results.
Every positive number has two square roots, one positive and one negative. They are opposites of each other.
Principal square root
(
[link] )
If
is a positive real number, then
represents the positive square root of
. The positive square root of a number is called the
principal square root of the number.
Secondary square root
(
[link] )
represents the negative square root of
. The negative square root of a number is called the
secondary square root of the number.
Radical sign, radicand; and radical (
[link] )
In the expression
√ is called the
radical sign .
is called the
radicand .
is called a
radical .
The horizontal bar that appears attached to the radical sign, √, is a grouping symbol that specifies the radicand.
Meaningful expressions (
[link] )
A radical expression will only be meaningful if the radicand (the expression under the radical sign) is
not negative:
is not meaningful and
is not a real number
Simplifying square root expressions (
[link] )
If
is a nonnegative number, then
Perfect squares (
[link] )
Real numbers that are squares of rational numbers are called
perfect squares .
Irrational numbers (
[link] )
Any indicated square root whose radicand is not a perfect square is an irrational number.
and
are irrational numbers
The product property (
[link] )
The quotient property (
[link] )
Be careful (
[link] )
A square root that does not involve fractions is in simplified form if there are no perfect squares in the radicand.
A square root involving a fraction is in simplified form if there are no
- perfect squares in the radicand,
- fractions in the radicand, or
- square root expressions in the denominator
Rationalizing the denominator (
[link] )
The process of eliminating radicals from the denominator is called
rationalizing the denominator .
Multiplying square root expressions (
[link] )
The product of the square roots is the square root of the product.
- Simplify each square root, if necessary.
- Perform the multiplication.
- Simplify, if necessary.
Dividing square root expressions (
[link] )
The quotient of the square roots is the square root of the quotient.
Addition and subtraction of square root expressions (
[link] )
Square root equation (
[link] )
A
square root equation is an equation that contains a variable under a square root radical sign.
Solving square root equations (
[link] )
- Isolate a radical.
- Square both sides of the equation.
- Simplify by combining like terms.
- Repeat step 1 if radical are still present.
- Obtain potential solution by solving the resulting non-square root equation.
- Check potential solutions by substitution.
Questions & Answers
how does Neisseria cause meningitis
is the branch of biology that deals with the study of microorganisms.
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
How bacteria create energy to survive?
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
which site have a normal flora
Many sites of the body have it
Skin
Nasal cavity
Oral cavity
Gastro intestinal tract
Safaa
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Binomial nomenclature
adeolu
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Source:
OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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