reducing square roots

Hello Again!!
sorry i dont know how to get a square root sign so I hope this makes sence, the question is...
Form an equivalent expression by rationalizing each denominator

the square root of 4
over
the square root of 27

=

the square root of 4
over
the square root of 9 times 3

=

the square root of 4
over
3 the square root of 3

i then multiple both the numerator and denominators by the square root of 3

=

the square root of 12
over
3 times 3

so i know have the square root of 12
over
9

so i factor the 12

(4) (3)
over
9

it then becomes 2 the square root of 3
over
9

does that sound right?

Looks good to me. Here's a slightly different approach.
\(\displaystyle \frac{\sqrt4}{\sqrt{27}}=\frac{2}{3\sqrt3}=\frac{2\sqrt3}{9}\)

thanks!!!!