SOLUTION: Why can't we rewrite the product as a whole radical, for instance {{{sqrt(8) * (root(4,27))}}}, wherein it is an incorrect simplification that the answer is {{{root(4,216^3)}}}? I

Algebra ->  Radicals -> SOLUTION: Why can't we rewrite the product as a whole radical, for instance {{{sqrt(8) * (root(4,27))}}}, wherein it is an incorrect simplification that the answer is {{{root(4,216^3)}}}? I      Log On


   

Question 1089099: Why can't we rewrite the product as a whole radical, for instance sqrt%288%29+%2A++%28root%284%2C27%29%29, wherein it is an incorrect simplification that the answer is root%284%2C216%5E3%29? I believe that the answer should be this one 2sqrt%282%29%28root%284%2C27%29%29. Please give me an explanation for this one. Thank you
Found 2 solutions by josgarithmetic, Alan3354:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%288%29%2A%28root%284%2C27%29%29%3C%3Eroot%284%2C216%5E3%29, UNEQUAL

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27=3%2A3%2A3=3%5E3
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root%284%2C27%29
root%284%2C3%5E3%29

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sqrt%288%29=sqrt%282%5E3%29=2sqrt%282%29
OR
2%2A2%5E%281%2F2%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Why can't we rewrite the product as a whole radical, for instance sqrt%288%29+%2A++%28root%284%2C27%29%29, wherein it is an incorrect simplification that the answer is root%284%2C216%5E3%29? I believe that the answer should be this one 2sqrt%282%29%28root%284%2C27%29%29.
==================
sqrt%288%29%2A%28root%284%2C27%29%29
= root%284%2C64%29%2A%28root%284%2C27%29%29
= root%284%2C1728%29
Or,
= 2root%284%2C4%29%2A%28root%284%2C27%29%29
= 2root%284%2C108%29
============
That can be written as:
= 2sqrt%282%29%2A%28root%284%2C27%29%29
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Which is simpler, or "more simplified," can be a matter of opinion.