SOLUTION: multiplication problem: (2 sqrt. 5xy) (2 sqrt. 10x^2y^3) thank you for your help!!

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Question 188724: multiplication problem:
(2 sqrt. 5xy) (2 sqrt. 10x^2y^3)
thank you for your help!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2Asqrt%285xy%29%29%282%2Asqrt%2810x%5E2y%5E3%29%29 Start with the given expression.


%282%2A2%29%2A%28sqrt%285xy%29%2Asqrt%2810x%5E2y%5E3%29%29 Rearrange the terms.


4%2A%28sqrt%285xy%29%2Asqrt%2810x%5E2y%5E3%29%29 Multiply 2 and 2 to get 4


4%2Asqrt%28%285xy%29%2810x%5E2y%5E3%29%29 Combine the roots using the identity sqrt%28x%29%2Asqrt%28y%29=sqrt%28x%2Ay%29


4%2Asqrt%28%285%2A10%29%28xy%2Ax%5E2y%5E3%29%29 Rearrange the terms inside the root.


4%2Asqrt%2850xy%2Ax%5E2y%5E3%29 Multiply 5 and 10 to get 50


4%2Asqrt%2850x%5E%281%2B2%29y%5E%281%2B3%29%29 Multiply the variable terms by adding the exponents.


4%2Asqrt%2850x%5E3y%5E4%29 Add


4%2Asqrt%2825%2A2%2Ax%5E3%2Ay%5E4%29 Factor 50 into 25%2A2


4%2Asqrt%2825%2A2%2Ax%5E2%2Ax%2Ay%5E4%29 Factor x%5E3 into x%5E2%2Ax


4%2Asqrt%2825%2A2%2Ax%5E2%2Ax%2Ay%5E2%2Ay%5E2%29 Factor y%5E4 into y%5E2%2Ay%5E2


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


4%2A5%2Asqrt%282%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29 Take the square root of 25 to get 5.


20%2Asqrt%282%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29 Multiply 4 and 5 to get 20


20%2Asqrt%282%29%2Ax%2Asqrt%28x%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29 Take the square root of x%5E2 to get x.


20%2Asqrt%282%29%2Ax%2Asqrt%28x%29%2Ay%2Ay Take the square root of y%5E2 to get y.


20xy%5E2%2Asqrt%282x%29 Rearrange and multiply the terms.

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Answer:


So %282%2Asqrt%285xy%29%29%282%2Asqrt%2810x%5E2y%5E3%29%29 simplifies to 20xy%5E2%2Asqrt%282x%29


In other words, %282%2Asqrt%285xy%29%29%282%2Asqrt%2810x%5E2y%5E3%29%29=20xy%5E2%2Asqrt%282x%29 where every variable is non-negative.