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- Elementary algebra
- Roots, radicals, and square root
- Simplifying square root expressions
To simplify a square root expression that does not involve a fraction, we can use the following two rules:
Simplifying square roots without fractions
- If a factor of the radicand contains a variable with an
even exponent, the square root is obtained by dividing the exponent by 2.
- If a factor of the radicand contains a variable with an
odd exponent, the square root is obtained by first factoring the variable factor into two factors so that one has an even exponent and the other has an exponent of 1, then using the product property of square roots.
Sample set a
Simplify each square root.
Both exponents are even:
and
The exponent on the square root of
is 3. The exponent on the square root if
is 5.
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Practice set a
Simplify each square root.
Square roots involving fractions
A square root expression is in simplified form if there are
- no perfect squares in the radicand,
- no fractions in the radicand, or
- 3. no square root expressions in the denominator.
The square root expressions
and
are in simplified form.
The square root expressions
and
are
not in simplified form.
Simplifying square roots with fractions
To simplify the square root expression
- Write the expression as
using the rule
- Multiply the fraction by 1 in the form of
- Simplify the remaining fraction,
Rationalizing the denominator
The process involved in step 2 is called
rationalizing the denominator. This process removes square root expressions from the denominator using the fact that
Sample set b
Simplify each square root.
Practice set b
Simplify each square root.
Exercises
For the following problems, simplify each of the radical expressions.
Exercises for review
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
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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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