SOLUTION: Simplify the radical . Assume that all variables represent positive numbers. square root 8xy^2 ___________ _________ square root 5xy Explain in detail please? Than

Algebra ->  Radicals -> SOLUTION: Simplify the radical . Assume that all variables represent positive numbers. square root 8xy^2 ___________ _________ square root 5xy Explain in detail please? Than      Log On


   

Question 37794: Simplify the radical . Assume that all variables represent positive numbers.


square root 8xy^2
_____________________
square root 5xy
Explain in detail please?
Thank you
Answer by junior403(76) About Me  (Show Source):
You can put this solution on YOUR website!
So we need to simplify the radical...
sqrt%288xy%5E2%29%2F+sqrt%285xy%29%29+
According to the quotient rule for radicals we need to eliminate the radical sign in the denominator by rationalizing the expression (simply multiplying both the numerator and the denominator by the denominator)Thus creating a square root of a square.
Sounds confusing but its really simple...
%28sqrt%288xy%5E2%29%2F+sqrt%285xy%29%29+%28sqrt%285xy%29%2F+sqrt%285xy%29%29= %28sqrt%2840x%5E2y%5E3%29%2F+sqrt%28%285xy%29%29%5E2%29+ = %28sqrt%2840x%5E2y%5E3%29%2F+5xy%29+
Now we just have to simplify the numerator...
40 = 10 * 4 and 4 is a square 2%5E2so it comes out from under the radical as 2%2Asqrt+%2810x%5E2y%5E3%29
The same with x%5E2 comes out as 2x%2Asqrt+%2810y%5E3%29
Then the y%5E3 comes out as 2xy%2Asqrt+%2810y%29
So we now have...
2xy%2Asqrt%2810y%29%2F+5xy%29+
And this can be reduced further by canceling the xy variables...
The final result is...
2%2Asqrt%2810y%29%2F+5%29+
I hope this helps!
Good Luck!