So √27 / √75 =

the top first √27 = √9 * √3 =                3 * √3

now the bottom part √75 = √25 * √3 = 5 * √3

and so the √3 cancells out leaving       = 3/5

√(ab) = √a · √b
√(a/b) = (√a) / (√b)
~~~~~~~~
√(27/75) = (√27)/(√75) = (√(3 · 9)) / (√(3 · 25)) = 3√3 / 5√3 = 3/5
   3 √3   
   5 √3  
    3      
    5  

sqrt(27/75)

= sqrt(9/25), after cancelling 3.

= 3/5 <==Answer, since (3/5)^2 = 9/25