SOLUTION: √(12z^10 ) Rewrite in simplified radical form, assume that all variables represent positive real numbers

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Question 294173: √(12z^10 ) Rewrite in simplified radical form, assume that all variables represent positive real numbers
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2812%2Az%5E10%29 Start with the given expression.


sqrt%284%2A3%2Az%5E10%29 Factor 12 into 4%2A3


sqrt%284%2A3%2A%28z%5E5%29%5E2%29 Rewrite z%5E10 into %28z%5E5%29%5E2


sqrt%284%29%2Asqrt%283%29%2Asqrt%28%28z%5E5%29%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%28%28z%5E5%29%5E2%29 Take the square root of 4 to get 2.


2z%5E5%2Asqrt%283%29 Take the square root of %28z%5E5%29%5E2 to get z%5E5 and rearrange the terms.

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Answer:


So sqrt%2812%2Az%5E10%29 simplifies to 2z%5E5%2Asqrt%283%29


In other words, sqrt%2812%2Az%5E10%29=2z%5E5%2Asqrt%283%29 where z%3E=0.