SOLUTION: i need to the square root of 20t^6 and simplify it in radical form

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Question 201562: i need to the square root of 20t^6 and simplify it in radical form
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2820%2At%5E6%29 Start with the given expression.


sqrt%284%2A5%2At%5E6%29 Factor 20 into 4%2A5


sqrt%284%2A5%2At%5E2%2At%5E2%2At%5E2%29 Factor t%5E6 into t%5E2%2At%5E2%2At%5E2


sqrt%284%29%2Asqrt%285%29%2Asqrt%28t%5E2%29%2Asqrt%28t%5E2%29%2Asqrt%28t%5E2%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


2%2Asqrt%285%29%2Asqrt%28t%5E2%29%2Asqrt%28t%5E2%29%2Asqrt%28t%5E2%29 Take the square root of 4 to get 2.


2%2Asqrt%285%29%2At%2At%2At Take the square root of t%5E2 to get t.


2t%5E3%2Asqrt%285%29 Multiply and rearrange the terms.

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Answer:


So sqrt%2820%2At%5E6%29 simplifies to 2t%5E3%2Asqrt%285%29


In other words, sqrt%2820%2At%5E6%29=2t%5E3%2Asqrt%285%29 where every variable is non-negative.


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