SOLUTION: Hi can you help with this one? Multiply and then simplify by factoring, if possible. Square root of 2x times square root of 16y Thanks!

Algebra ->  Square-cubic-other-roots -> SOLUTION: Hi can you help with this one? Multiply and then simplify by factoring, if possible. Square root of 2x times square root of 16y Thanks!      Log On


   

Question 249020: Hi can you help with this one?
Multiply and then simplify by factoring, if possible.
Square root of 2x times square root of 16y
Thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282x%29%2Asqrt%2816y%29 Start with the given expression.


sqrt%282x%29%2Asqrt%2816%29%2Asqrt%28y%29 Break up the second square root using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29


sqrt%282x%29%2A4%2Asqrt%28y%29 Take the square root of 16 to get 4.


4%2Asqrt%282x%29%2Asqrt%28y%29 Rearrange the terms.


4%2Asqrt%282xy%29 Combine the roots using the identity sqrt%28x%29%2Asqrt%28y%29=sqrt%28x%2Ay%29



So sqrt%282x%29%2Asqrt%2816y%29=4%2Asqrt%282xy%29 where 'x' and 'y' are non-negative.