Let's analyze and simplify the given expression:

$z = \frac{\sqrt{72}}{3} - 2\sqrt{128} + 9\sqrt{2} \times \sqrt{18} - 3$

Step-by-Step Solution:

1. Simplify the square roots:

   • $\sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2}$
   • $\sqrt{128} = \sqrt{64 \times 2} = 8\sqrt{2}$
   • $\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$

   Substituting these simplified forms back:

   $z = \frac{6\sqrt{2}}{3} - 2(8\sqrt{2}) + 9\sqrt{2} \times 3\sqrt{2} - 3$

2. Perform operations:

   • $\frac{6\sqrt{2}}{3} = 2\sqrt{2}$
   • $-2(8\sqrt{2}) = -16\sqrt{2}$
   • $9\sqrt{2} \times 3\sqrt{2} = 27 \times 2 = 54$
   • The constant term remains $-3$.

   Substituting these results:

   $z = 2\sqrt{2} - 16\sqrt{2} + 54 - 3$

3. Combine like terms:

   • Combine the $\sqrt{2}$ terms: $2\sqrt{2} - 16\sqrt{2} = -14\sqrt{2}$
   • Combine the constants: $54 - 3 = 51$

   Therefore:

   $z = -14\sqrt{2} + 51$

Final Answer:

$z = 51 - 14\sqrt{2}$

Let me know if you need further clarifications or details on this!

Here are five questions for practice:

1. How would you simplify the expression $\sqrt{50} + \sqrt{8}$?
2. What are the properties of square roots when multiplying or dividing terms?
3. How can constants and radicals be combined effectively in expressions?
4. Solve a similar problem: $\frac{\sqrt{48}}{4} - \sqrt{75}$.
5. Can $\sqrt{x^2}$ always be simplified as $x$? Why or why not?

Tip: Always look for perfect squares within a radical to simplify it easily!