SOLUTION: Please help. I need to simplify square root 2t^5 times square root10t^4 Thanks in advance!

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Question 88353: Please help.
I need to simplify square root 2t^5 times square root10t^4
Thanks in advance!
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282t%5E5%29sqrt%2810t%5E4%29

sqrt%282t%5E5%2A10t%5E4%29 Combine the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

sqrt%2820t%5E9%29 Multiply



sqrt%284%2A5%2At%5E9%29 Factor 20 into 4%2A5

sqrt%284%2A5%2At%2At%5E2%2At%5E2%2At%5E2%2At%5E2%29 Factor t%5E9 into t%2At%5E2%2At%5E2%2At%5E2%2At%5E2

sqrt%284%29%2Asqrt%285%29%2Asqrt%28t%29%2Asqrt%28t%5E2%29%2Asqrt%28t%5E2%29%2Asqrt%28t%5E2%29%2Asqrt%28t%5E2%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

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

2%2Asqrt%285%29%2Asqrt%28t%29%2At%2At%2At%2At Take the square root of each of the perfect squares t%5E2 to get t

2%2Asqrt%285%29%2At%5E4%2Asqrt%28t%29 Multiply the common terms
2%2At%5E4%2Asqrt%28t%29%2Asqrt%285%29 Rearrange the terms
2%2At%5E4%2Asqrt%285t%29 Group the square root terms




Check:
sqrt%282%283%29%5E5%29sqrt%2810%283%29%5E4%29 Plug in x=3 (any value will do)

sqrt%282%2A243%29sqrt%2810%2A81%29

%2822.04540%29%2828.46049%29

627.423


Now lets check our answer
2%2A%283%29%5E4%2Asqrt%285%283%29%29 Plug in x=3

2%2A%283%29%5E4%2Asqrt%2815%29

2%2A81%2Asqrt%2815%29

162%2Asqrt%2815%29

162%2A3.872983

627.423

works