SOLUTION: Simplify by factoring. √(245k^7 q^8 )

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Question 248009: Simplify by factoring. √(245k^7 q^8 )
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%28245%2Ak%5E7%2Aq%5E8%29 Start with the given expression.


sqrt%2849%2A5%2Ak%5E7%2Aq%5E8%29 Factor 245 into 49%2A5


sqrt%2849%2A5%2Ak%5E2%2Ak%5E2%2Ak%5E2%2Ak%2Aq%5E8%29 Factor k%5E7 into k%5E2%2Ak%5E2%2Ak%5E2%2Ak


sqrt%2849%2A5%2Ak%5E2%2Ak%5E2%2Ak%5E2%2Ak%2Aq%5E2%2Aq%5E2%2Aq%5E2%2Aq%5E2%29 Factor q%5E8 into q%5E2%2Aq%5E2%2Aq%5E2%2Aq%5E2


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


Take the square root of 49 to get 7.


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


7%2Asqrt%285%29%2Ak%2Ak%2Ak%2Asqrt%28k%29%2Aq%2Aq%2Aq%2Aq Take the square root of q%5E2 to get q.


7k%5E3q%5E4%2Asqrt%285k%29 Rearrange and multiply the terms.

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Answer:


So sqrt%28245%2Ak%5E7%2Aq%5E8%29 simplifies to 7k%5E3q%5E4%2Asqrt%285k%29


In other words, sqrt%28245%2Ak%5E7%2Aq%5E8%29=7k%5E3q%5E4%2Asqrt%285k%29 where every variable is non-negative.