How do you write the expression with a rationalized denominator for 3√2/3√6?

To rationalize the denominator of the expression 3√2 / 3√6, we want to eliminate the square root in the denominator. The steps to achieve this are as follows:

1. Write the original expression:
   
   It starts as 3√2 / 3√6.
2. Identify the denominator:
   
   In this case, the denominator is 3√6.
3. Multiply the numerator and denominator by the conjugate:
   
   Here, the conjugate of 3√6 is **√6**. Therefore, we multiply both the numerator and the denominator by **√6**:
4. Perform the multiplication:
   
   We get the following:
• Numerator: 3√2 * √6 = 3√(2 * 6) = 3√12 = 6√3
• Denominator: 3√6 * √6 = 3 * 6 = 18
5. Combine the results: You now have the expression as:

6√3 / 18

6. Simplify the expression:

   To simplify, we divide both numerator and denominator by 6:

   (6/6)√3 / (18/6) = √3 / 3

So, the rationalized form of 3√2 / 3√6 is √3 / 3.