SOLUTION: the directions are: Simplify. Assume that varibles represnt positive real numbers. can you please help me with. ^3 inside the square root symbol is (27y^3/z^4) I blieve tha

Algebra ->  Algebra  -> Radicals -> SOLUTION: the directions are: Simplify. Assume that varibles represnt positive real numbers. can you please help me with. ^3 inside the square root symbol is (27y^3/z^4) I blieve tha      Log On

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Question 148091: the directions are: Simplify. Assume that varibles represnt positive real numbers.
can you please help me with. ^3 inside the square root symbol is (27y^3/z^4)
I blieve that the top number is 3y, but I don't know how you take the fourth power when the radital is rasied to a 3.
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28%2827y%5E3%29%2F%28z%5E4%29%29 Start with the given expression.


%28sqrt%2827y%5E3%29%29%2F%28sqrt%28z%5E4%29%29 Break up the root.


%28sqrt%283%5E2%2A3%2Ay%5E2%2Ay%29%29%2F%28sqrt%28z%5E4%29%29 Factor 27y%5E3 into 3%5E2%2A3%2Ay%5E2%2Ay


%28sqrt%283%5E2%2A3%2Ay%5E2%2Ay%29%29%2F%28sqrt%28z%5E2%2Az%5E2%29%29 Factor z%5E4 into z%5E2%2Az%5E2


%28sqrt%283%5E2%29%2Asqrt%283%29%2Asqrt%28y%5E2%29%2Asqrt%28y%29%29%2F%28sqrt%28z%5E2%29%2Asqrt%28z%5E2%29%29 Break up the square roots.


%283%2Asqrt%283%29%2Ay%2Asqrt%28y%29%29%2F%28z%2Az%29 Evaluate sqrt%283%5E2%29 to get 3. Evaluate sqrt%28y%5E2%29 to get y. Evaluate sqrt%28z%5E2%29 to get z. So the square root of anything squared is itself (assuming the variable is positive)



%283y%2Asqrt%283y%29%29%2F%28z%5E2%29 Multiply and combine the roots.


So sqrt%28%2827y%5E3%29%2F%28z%5E4%29%29 simplifies to %283y%2Asqrt%283y%29%29%2F%28z%5E2%29


In other words, sqrt%28%2827y%5E3%29%2F%28z%5E4%29%29=%283y%2Asqrt%283y%29%29%2F%28z%5E2%29 where every variable is positive and z%3C%3E0