SOLUTION: Simplify sqrt 12c^6

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Question 200951: Simplify
sqrt 12c^6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2812%2Ac%5E6%29 Start with the given expression.


sqrt%284%2A3%2Ac%5E6%29 Factor 12 into 4%2A3


sqrt%284%2A3%2Ac%5E2%2Ac%5E2%2Ac%5E2%29 Factor c%5E6 into c%5E2%2Ac%5E2%2Ac%5E2


sqrt%284%29%2Asqrt%283%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


2%2Asqrt%283%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29%2Asqrt%28c%5E2%29 Take the square root of 4 to get 2.


2%2Asqrt%283%29%2Ac%2Ac%2Ac Take the square root of c%5E2 to get c.


2c%5E3%2Asqrt%283%29 Rearrange and combine the terms.

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Answer:


So sqrt%2812%2Ac%5E6%29 simplifies to 2c%5E3%2Asqrt%283%29


In other words, sqrt%2812%2Ac%5E6%29=2c%5E3%2Asqrt%283%29 where c%3E=0.