SOLUTION: Simplify completely, keep answer in radical form. sqrt(24x^8y^3)/sqrt(75x^-7y^17)

Algebra ->  Expressions -> SOLUTION: Simplify completely, keep answer in radical form. sqrt(24x^8y^3)/sqrt(75x^-7y^17)       Log On


   

Question 1192820: Simplify completely, keep answer in radical form.
sqrt(24x^8y^3)/sqrt(75x^-7y^17)
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%2824x%5E8y%5E3%29%29%2F%28sqrt%2875x%5E-7y%5E17%29%29
Expand to show the perfect squares, reciprocal gets rid of the neg exponent

Extract the squares

Combine like terms
%282x%5E7%2Asqrt%286y%29%29%2F%285y%5E7sqrt%283%2A%281%2Fx%29%2Ay%29%29

Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


There are several different paths you can take to simplify this expression. I would definitely go a different direction that the other tutor. And according to usual standards, my simplified form should not have a radical in the denominator.

(1) Change the fraction containing square roots in numerator and denominator into a single square root of a fraction:



(2) Simplify the fraction:

sqrt%288x%5E15%2F25y%5E14%29

(3) Extract perfect squares where possible:

sqrt%28%284x%5E14%29%282x%29%2F25y%5E14%29+=+%282x%5E7%2F5y%5E7%29sqrt%282x%29