Question 37794
So we need to simplify the radical...
{{{sqrt(8xy^2)/ sqrt(5xy)) }}}
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...
{{{(sqrt(8xy^2)/ sqrt(5xy)) }}}{{{(sqrt(5xy)/ sqrt(5xy))}}}= {{{(sqrt(40x^2y^3)/ sqrt((5xy))^2) }}} = {{{(sqrt(40x^2y^3)/ 5xy) }}}
Now we just have to simplify the numerator...
40 = 10 * 4 and 4 is a square {{{2^2}}}so it comes out from under the radical as {{{2*sqrt (10x^2y^3)}}}
The same with {{{x^2}}} comes out as {{{2x*sqrt (10y^3)}}}
Then the {{{y^3}}} comes out as {{{2xy*sqrt (10y)}}}
So we now have...
{{{2xy*sqrt(10y)/ 5xy) }}}
And this can be reduced further by canceling the xy variables...
The final result is...
{{{2*sqrt(10y)/ 5) }}}  
I hope this helps!
Good Luck!