document.write( "Question 1004514: Which expression is NOT equivalent to 4(sqrt 4n^2)?\r
\n" ); document.write( "\n" ); document.write( " a. (4n^2)^1/4
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\n" ); document.write( " c. (2n)^1/2
\n" ); document.write( " d. (sqrt 2n)
\n" ); document.write( "I know that a. IS equivalent, but I'm not sure how to figure out the others.
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Algebra.Com's Answer #621001 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
as far as i can tell, none of them are equivalent to 4 * (sqrt(4n^2)).\r
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\n" ); document.write( "\n" ); document.write( "however, 3 out of the 4 selections are equivalent to each other, while the 4th one is not.\r
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\n" ); document.write( "\n" ); document.write( "that says there's something wrong with your original expression the way you showed it.\r
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\n" ); document.write( "\n" ); document.write( "your original expression is shown as 4(sqrt 4n^2)\r
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\n" ); document.write( "\n" ); document.write( "i read this as 4 times the square root of (4n^2).\r
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\n" ); document.write( "\n" ); document.write( "i believe you mean the fourth root of (4n^2).\r
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\n" ); document.write( "\n" ); document.write( "that would be written as any of the possible ways:\r
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\n" ); document.write( "\n" ); document.write( "root(4,4n^2) *****\r
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\n" ); document.write( "\n" ); document.write( "***** this is the official representation for algebra.com that you would use when graphing the fourth root of (4n^2).\r
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\n" ); document.write( "\n" ); document.write( "4root(4n^2)\r
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\n" ); document.write( "\n" ); document.write( "fourth root of (4n^2).\r
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\n" ); document.write( "\n" ); document.write( "if my assumption is correct, then the correct answer is selection b.\r
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\n" ); document.write( "\n" ); document.write( "selection b is not equivalent to fourth root of (4n^2).\r
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\n" ); document.write( "\n" ); document.write( "what you want to match is fourth root of (4n^2)\r
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\n" ); document.write( "\n" ); document.write( "selection a is (4n^2)^(1/4)\r
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\n" ); document.write( "\n" ); document.write( "just by definition, the fourth root of anything is equal to anything raised to the 1/4th power.\r
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\n" ); document.write( "\n" ); document.write( "that can be written as root(4,x) = x^(1/4)\r
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\n" ); document.write( "\n" ); document.write( "selection c is (2n)^(1/2)\r
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\n" ); document.write( "\n" ); document.write( "if you square the inside term and you take the square root of the outside term, you will get:\r
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\n" ); document.write( "\n" ); document.write( "(2n)^(1/2) = ((2n)^2)^(1/4)\r
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\n" ); document.write( "\n" ); document.write( "since (2n)^2 is equal to 4n^2, then the expression will become:\r
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\n" ); document.write( "\n" ); document.write( "(2n)^(1/2) = (4n^2)^(1/4)\r
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\n" ); document.write( "\n" ); document.write( "(4n^2)^(1/4) is the same as fourth root of (4n^2), so selection c is good.\r
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\n" ); document.write( "\n" ); document.write( "selection d is sqrt(2n)\r
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\n" ); document.write( "\n" ); document.write( "since sqrt(2n) is the same as (2n)^(1/2 and that's what selection c was, selection d is good as well.\r
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\n" ); document.write( "\n" ); document.write( "now to selection b.\r
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\n" ); document.write( "\n" ); document.write( "selection b is 2n^(1/2)\r
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\n" ); document.write( "\n" ); document.write( "that's equivalent to 2 * n^(1/2)\r
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\n" ); document.write( "\n" ); document.write( "2 is equal to 4^(1/2), so the expression becomes 4^(1/2) * n^(1/2)\r
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\n" ); document.write( "\n" ); document.write( "that is equivalent to (4n)^(1/2)\r
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\n" ); document.write( "\n" ); document.write( "if you square the inside term and take the squre root of the outsiee term, you get:\r
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\n" ); document.write( "\n" ); document.write( "(4n)^(1/2) is equivalent to ((4n)^2)^(1/4) which is equivalent to (16n^2)^(1/4)\r
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\n" ); document.write( "\n" ); document.write( "(16n^2)^(1/4) is not equivalent to (4n^2)^(1/4) so selection b is not good.\r
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\n" ); document.write( "\n" ); document.write( "you need to be well versed in the properties of exponents and roots to figure this out.\r
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\n" ); document.write( "\n" ); document.write( "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.\r
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\n" ); document.write( "\n" ); document.write( "for example:\r
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\n" ); document.write( "\n" ); document.write( "assume n = 3\r
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\n" ); document.write( "\n" ); document.write( "when n = 3:\r
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\n" ); document.write( "\n" ); document.write( "fourth root of (4n^2) is equal to 2.449489743\r
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\n" ); document.write( "\n" ); document.write( "selection a gives you (4n^2)^(1/4) = 2.449489743
\n" ); document.write( "selection b gives you 2n^(1/2) = 6
\n" ); document.write( "selection c gives you (2n)^(1/2) = 2.449489743
\n" ); document.write( "selection d gives you sqrt(2n) = 2.449489743\r
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\n" ); document.write( "\n" ); document.write( "all selections except selection b give you the same answer.\r
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\n" ); document.write( "\n" ); document.write( "here's some good tutorials on exponents and roots you might find useful if you care to take the time out to review them.\r
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\n" ); document.write( "\n" ); document.write( "http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut26_exp.htm\r
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\n" ); document.write( "\n" ); document.write( "http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut38_ratexp.htm\r
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