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Question 1004514: Which expression is NOT equivalent to 4(sqrt 4n^2)?
a. (4n^2)^1/4
b. 2n^1/2
c. (2n)^1/2
d. (sqrt 2n)
I know that a. IS equivalent, but I'm not sure how to figure out the others.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! as far as i can tell, none of them are equivalent to 4 * (sqrt(4n^2)).
however, 3 out of the 4 selections are equivalent to each other, while the 4th one is not.
that says there's something wrong with your original expression the way you showed it.
your original expression is shown as 4(sqrt 4n^2)
i read this as 4 times the square root of (4n^2).
i believe you mean the fourth root of (4n^2).
that would be written as any of the possible ways:
root(4,4n^2) *****
***** this is the official representation for algebra.com that you would use when graphing the fourth root of (4n^2).
4root(4n^2)
fourth root of (4n^2).
if my assumption is correct, then the correct answer is selection b.
selection b is not equivalent to fourth root of (4n^2).
what you want to match is fourth root of (4n^2)
selection a is (4n^2)^(1/4)
just by definition, the fourth root of anything is equal to anything raised to the 1/4th power.
that can be written as root(4,x) = x^(1/4)
selection c is (2n)^(1/2)
if you square the inside term and you take the square root of the outside term, you will get:
(2n)^(1/2) = ((2n)^2)^(1/4)
since (2n)^2 is equal to 4n^2, then the expression will become:
(2n)^(1/2) = (4n^2)^(1/4)
(4n^2)^(1/4) is the same as fourth root of (4n^2), so selection c is good.
selection d is sqrt(2n)
since sqrt(2n) is the same as (2n)^(1/2 and that's what selection c was, selection d is good as well.
now to selection b.
selection b is 2n^(1/2)
that's equivalent to 2 * n^(1/2)
2 is equal to 4^(1/2), so the expression becomes 4^(1/2) * n^(1/2)
that is equivalent to (4n)^(1/2)
if you square the inside term and take the squre root of the outsiee term, you get:
(4n)^(1/2) is equivalent to ((4n)^2)^(1/4) which is equivalent to (16n^2)^(1/4)
(16n^2)^(1/4) is not equivalent to (4n^2)^(1/4) so selection b is not good.
you need to be well versed in the properties of exponents and roots to figure this out.
another way less troublesome would be to just give a random number to n and then see which solutions are equivalent or not, using your calculator.
for example:
assume n = 3
when n = 3:
fourth root of (4n^2) is equal to 2.449489743
selection a gives you (4n^2)^(1/4) = 2.449489743
selection b gives you 2n^(1/2) = 6
selection c gives you (2n)^(1/2) = 2.449489743
selection d gives you sqrt(2n) = 2.449489743
all selections except selection b give you the same answer.
here's some good tutorials on exponents and roots you might find useful if you care to take the time out to review them.
http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut26_exp.htm
http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut38_ratexp.htm
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