SOLUTION: Simplify sqrt(27 c^5 d^10 e^9)

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Question 175900: Simplify sqrt(27 c^5 d^10 e^9)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2827c%5E5%2Ad%5E10%2Ae%5E9%29 Start with the given expression.


sqrt%2827c%5E4%2Ac%2Ad%5E10%2Ae%5E8%2Ae%29 Factor c%5E5 to get c%5E4%2Ac. Factor c%5E5 to get e%5E8%2Ae.


Break up the square root.


Simplify sqrt%2827%29 to get 3%2Asqrt%283%29


3%2Asqrt%283%29%2Ac%5E2%2Asqrt%28c%29%2Asqrt%28d%5E10%29%2Asqrt%28e%5E8%29%2Asqrt%28e%29 Take the square root of c%5E4 to get c%5E2 (notice how the exponent is cut it in half)


3%2Asqrt%283%29%2Ac%5E2%2Asqrt%28c%29%2Ad%5E5%2Asqrt%28e%5E8%29%2Asqrt%28e%29 Take the square root of d%5E10 to get d%5E5 (notice how the exponent is cut it in half)


3%2Asqrt%283%29%2Ac%5E2%2Asqrt%28c%29%2Ad%5E5%2Ae%5E4%2Asqrt%28e%29 Take the square root of e%5E8 to get e%5E4 (notice how the exponent is cut it in half)



3c%5E2%2Ad%5E5%2Ae%5E4%2Asqrt%283ce%29 Recombine the radicals.


So sqrt%2827c%5E5%2Ad%5E10%2Ae%5E9%29 simplifies to 3c%5E2%2Ad%5E5%2Ae%5E4%2Asqrt%283ce%29