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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 the planets on our solar system orbit
how many Messier objects are there in space
Astronomy (from Ancient Greek ἀστρονομία (astronomía) 'science that studies the laws of the stars') is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution.
Rafael
what is big bang theory?
Rosemary
what type of activity astronomer do?
Rosemary
the big bang theory is a theory which states that all matter was compressed together in one place the matter got so unstable it exploded releasing All its contents in the form of hydrogen
Roaul
I want to be an astronomer. That's my dream
Astrit
Who named the the whole galaxy?
what is the dark matter
Richard
what are the factors upon which the atmosphere is stratified
bigbang is the beginning of the universe
Sokak
but thats just a theory
Sokak
nothing will happen, don't worry brother.
Vansh
these are Rocky substances between mars and jupiter
GANGAIN
Comets are cosmic snowballs of frozen gases , rock and dust that orbit the sun. They are mostly found between the orbits of Venus and Mercury.
Aarya
hey can anyone guide me abt international astronomy olympiad
sahil
how can we learn right and true ?
why the moon is always appear in an elliptical shape
Because when astroid hit the Earth then a piece of elliptical shape of the earth was separated which is now called moon.
Hemen
Did you mean eye sight or sea level
Minal
oh sorry it's sea level
lidiya
according to the theory of astronomers why the moon is always appear in an elliptical orbit?
Gatjuol
hi !!! I am new in astronomy....
I have so many questions in mind ....
all of scientists of the word they just give opinion only.
but they never think true or false ...
i respect all of them...
I believes whole universe depending
on true ...থিউরি
Govinda
we're all stars and galaxies a part of sun. how can science prove thx with respect old ancient times picture or books..or anything with respect to present time .but we r a part of that universe
w astronomy and cosmology!
Michele
another theory of universe except big ban
there many theory to born universe but what is the reality of big bang theory to born universe
Asmit
what is the exact value of π?
Nagalakshmi
there are many theories regarding this it's on you believe any theory that you think is true ex. eternal inflation theory, oscillation model theory, multiple universe theory the big bang theory etc.
Aarya
I think after Big Bang!
Michele
from where on earth could u observe all the stars during the during the course of an year
I think it couldn't possible on earth
Nagalakshmi
in this time i don't Know
Michele
is that so. the question was in the end of this chapter
Karuna
in theory, you could see them all from the equator (though over the course of a year, not at pne time). stars are measured in "declination", which is how far N or S of the equator (90* to -90*). Polaris is the North star, and is ALMOST 90* (+89*).
So it would just barely creep over the horizon.
Christopher
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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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