SOLUTION: how to figure out this problem-- dividing radical expressions square root 3x squared y cubed over 4 square root 5xy cubed I hope you understand what I'm trying to say

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Question 176549: how to figure out this problem-- dividing radical expressions
square root 3x squared y cubed over 4 square root 5xy cubed
I hope you understand what I'm trying to say
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
First, simplify sqrt%283x%5E2y%5E3%29


sqrt%283x%5E2y%5E3%29=sqrt%283x%5E2y%5E2%2Ay%29=sqrt%283%29%2Asqrt%28x%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%29=sqrt%283%29%2Ax%2Ay%2Asqrt%28y%29=xy%2Asqrt%283y%29


So sqrt%283x%5E2y%5E3%29=xy%2Asqrt%283y%29 where every variable is positive.


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Now simplify sqrt%285xy%5E3%29


sqrt%285xy%5E3%29=sqrt%285xy%5E2%2Ay%29=sqrt%285%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29%2Asqrt%28y%29=sqrt%285%29%2Asqrt%28x%29%2Ay%2Asqrt%28y%29=y%2Asqrt%285xy%29


So sqrt%285xy%5E3%29=y%2Asqrt%285xy%29 where every variable is positive.


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So

sqrt%283x%5E2y%5E3%29%2F%284%2Asqrt%285xy%5E3%29%29


simplifies to


%28xy%2Asqrt%283y%29%29%2F%284%2Ay%2Asqrt%285xy%29%29


%28x%2Ahighlight%28y%29%2Asqrt%283y%29%29%2F%284%2Ahighlight%28y%29%2Asqrt%285xy%29%29 Highlight the common terms.


%28x%2Across%28y%29%2Asqrt%283y%29%29%2F%284%2Across%28y%29%2Asqrt%285xy%29%29 Cancel out the common terms.


%28x%2Asqrt%283y%29%29%2F%284%2Asqrt%285xy%29%29 Simplify


%28x%2Asqrt%283y%29%2Asqrt%285xy%29%29%2F%284%2Asqrt%285xy%29%2Asqrt%285xy%29%29 Multiply the numerator and denominator by sqrt%285xy%29 (to rationalize the denominator)


%28x%2Asqrt%283y%29%2Asqrt%285xy%29%29%2F%284%2A5xy%29 Multiply sqrt%285xy%29 by itself to get sqrt%285xy%29%2Asqrt%285xy%29=%28sqrt%285xy%29%29%5E2=5xy


%28x%2Asqrt%283y%2A5xy%29%29%2F%284%2A5xy%29 Combine the radicals


%28x%2Asqrt%2815xy%5E2%29%29%2F%2820xy%29 Multiply


%28cross%28x%29%2Asqrt%2815xy%5E2%29%29%2F%2820%2Across%28x%29y%29 Cancel out like terms.


sqrt%2815xy%5E2%29%2F%2820y%29 Simplify


%28y%2Asqrt%2815x%29%29%2F%2820y%29 Simplify the square root.


%28cross%28y%29%2Asqrt%2815x%29%29%2F%2820cross%28y%29%29 Cancel out like terms.


sqrt%2815x%29%2F20



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Answer:


So after all of that, the solution is


sqrt%283x%5E2y%5E3%29%2F%284%2Asqrt%285xy%5E3%29%29=sqrt%2815x%29%2F20 where every variable is positive