SOLUTION: Write the following expression in simplified radical form sqrt75s^5t^10 Assume that all variables represent positives real numbers

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Question 376607: Write the following expression in simplified radical form
sqrt75s^5t^10
Assume that all variables represent positives real numbers
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2875%2As%5E5%2At%5E10%29 Start with the given expression.


sqrt%2825%2A3%2As%5E5%2At%5E10%29 Factor 75 into 25%2A3


sqrt%2825%2A3%2As%5E2%2As%5E2%2As%2At%5E10%29 Factor s%5E5 into s%5E2%2As%5E2%2As


sqrt%2825%2A3%2As%5E2%2As%5E2%2As%2At%5E2%2At%5E2%2At%5E2%2At%5E2%2At%5E2%29 Factor t%5E10 into t%5E2%2At%5E2%2At%5E2%2At%5E2%2At%5E2


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


Take the square root of 25 to get 5.


Take the square root of s%5E2 to get s.


5%2Asqrt%283%29%2As%2As%2Asqrt%28s%29%2At%2At%2At%2At%2At Take the square root of t%5E2 to get t.


5s%5E2t%5E5%2Asqrt%283s%29 Rearrange and multiply the terms.

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Answer:


So sqrt%2875%2As%5E5%2At%5E10%29 simplifies to 5s%5E2t%5E5%2Asqrt%283s%29


In other words, sqrt%2875%2As%5E5%2At%5E10%29=5s%5E2t%5E5%2Asqrt%283s%29 where every variable is non-negative.


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Jim