SOLUTION: Rewrite the following in simplified radical form -assume all variable represent positive real numbers √27v^12

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Question 582738: Rewrite the following in simplified radical form
-assume all variable represent positive real numbers
√27v^12

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2827%2Av%5E12+%29 Start with the given expression.


sqrt%289%2A3%2Av%5E12+%29 Factor 27 into 9%2A3


sqrt%289%2A3%2Av%5E2%2Av%5E2%2Av%5E2%2Av%5E2%2Av%5E2%2Av%5E2%29 Factor v%5E12+ into v%5E2%2Av%5E2%2Av%5E2%2Av%5E2%2Av%5E2%2Av%5E2


Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


Take the square root of 9 to get 3.


3%2Asqrt%283%29%2Av%2Av%2Av%2Av%2Av%2Av Take the square root of v%5E2 to get v.


3v%5E6%2Asqrt%283%29 Rearrange and multiply the terms.

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Answer:


So sqrt%2827%2Av%5E12+%29 simplifies to 3v%5E6%2Asqrt%283%29


In other words, sqrt%2827%2Av%5E12+%29=3v%5E6%2Asqrt%283%29 where every variable is non-negative.