answer these problems on dividing radicals

Question

1. √125/√5 2. √35/√2 3. √27x/√3x 4. 3/√2 5. √96a^7/√6a 6. 2x/√3 7. √8x^2/ √2 8. √12y/√3 9. √3xy/√6x

Answer 1

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 )