How can you write the expression with a rationalized denominator?

Question

((3sqrt2)/(3sqrt6))

A. (3sqrt9)/3

B. ((2+(3sqrt9)))/6

C. (3sqrt9)/6

D. (3sqrt72)/3

Answer 1

((3sqrt2)/(3sqrt6)) can be written as ((3sqrt2)/(3sqrt2*sqrt3)). To rationalize the denominator, we can multiply both numerator and denominator by sqrt3, which gives:

((3sqrt2)/(3sqrt2*sqrt3)) * (sqrt3/sqrt3)

Simplifying the numerator and denominator:

= (3sqrt6)/(3*sqrt(2*3))

= (3sqrt6)/(3sqrt6)

= 1

Therefore, the expression with a rationalized denominator is 1, which is not one of the answer choices listed.