To rationalize the denominator of 2√10/3√11, you should multiply the expression by which factor?

This is the concept of surds, we are required to rationalize the denominator of the (2sqrt10)/(3sqrt11)
torationalize the denominator we proceed as follows;
(2sqrt10)/(3sqrt11)
multiplying both the numerator and the denominator by 2sqrt11 we get:
[(2sqrt10)/(3sqrt11)]*[(3sqrt11)/(3sqrt11)]
=[2*3sqrt(11*10)]/(3*3*sqrt(11*11))
=[6sqrt110]/[3*3*11]
=[6sqrt110]/99
=[2sqrt110]/33
the answer is:
[2sqrt110]/33