sqrt(125)/sqrt(5) = sqrt(125/5) = sqrt(25) = +5 or -5
sqrt(35)/sqrt(2) = sqrt(35/2)
sqrt(27x) / (sqrt(3x) = sqrt( (27x) / (3x) ) = sqrt(9) = +3 or -3
3 / sqrt(2) = ( 3 * sqrt(2) ) / ( sqrt(2) * sqrt(2) ) = 3sqrt(2) / 2
sqrt(96a^7)/sqrt(6a) = sqrt( (96a^7) / (6a) ) = sqrt(16a^6) = +4a^3 or -4a^3
2x/sqrt(3) = ( 2x * sqrt(3) ) / ( sqrt(3) * sqrt(3) ) = 2sqrt(3)x / 3
sqrt(8x^2)/sqrt(2) = sqrt( (8x^2)/2 ) = sqrt(4x^2) = +2x or -2x
sqrt(12y)/sqrt(3) = sqrt( 12y/3 ) = sqrt(4y) = 2sqrt(y)
sqrt(3xy) / sqrt(6x) = sqrt( 3xy / 6x ) = sqrt( y / 2 )