What is the square root of 27x^3 divided by the square root of 3x (solve using the quotient rule)

Question

(√27x³)

———

(√3x)

Answer 1

√(27x^3)/√(3x)

√(27x^3/3x)

√9x^2 (27/3=9 and x^3/x=x^2)

both 9 and x^2 are perfect squares

the answer is 3x

Answer 2

((3x)^1/2(27x³/2)^-1/2 - (27x³)^1/2(3x/2)^-1/2)/3x

((3x)^1/2(2/27x³)^1/2 - (27x³)^1/2(2/3x)^1/2)/3x

(6x/27x³)^1/2 - (54x³/3x)^1/2)/3x

(2/9x²)^1/2/3x - (18x²)^1/2/3x

(2)^1/2(3x)/3x - 3x(2)^1/2/3x

(2)^1/2 - 9x²(2)^1/2

√2 - 9x²√2