SOLUTION: Use the product rule to simplify. All variables represent nonnegative real numbers. √20x^5y

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Question 309929: Use the product rule to simplify. All variables represent nonnegative real numbers.
√20x^5y
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2820%2Ax%5E5%2Ay%29 Start with the given expression.


sqrt%284%2A5%2Ax%5E5%2Ay%29 Factor 20 into 4%2A5


sqrt%284%2A5%2Ax%5E2%2Ax%5E2%2Ax%2Ay%29 Factor x%5E5 into x%5E2%2Ax%5E2%2Ax


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


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


2%2Asqrt%285%29%2Ax%2Ax%2Asqrt%28x%29%2Asqrt%28y%29 Take the square root of x%5E2 to get x.


2x%5E2%2Asqrt%285xy%29 Rearrange and multiply the terms.

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Answer:


So sqrt%2820%2Ax%5E5%2Ay%29 simplifies to 2x%5E2%2Asqrt%285xy%29


In other words, sqrt%2820%2Ax%5E5%2Ay%29=2x%5E2%2Asqrt%285xy%29 where every variable is non-negative.