The expression shown in the image is:

$3 \sqrt{3} \left( 4 \sqrt{3} + 3 \right)$

Let's simplify this step by step.

Step 1: Distribute $3 \sqrt{3}$ to both terms inside the parentheses.

$3 \sqrt{3} \times 4 \sqrt{3} + 3 \sqrt{3} \times 3$

Step 2: Multiply the first part: $3 \sqrt{3} \times 4 \sqrt{3}$.

$3 \times 4 \times \sqrt{3} \times \sqrt{3} = 12 \times 3 = 36$

Step 3: Multiply the second part: $3 \sqrt{3} \times 3$.

$3 \times 3 \times \sqrt{3} = 9 \sqrt{3}$

Step 4: Combine the results.

$36 + 9 \sqrt{3}$

Thus, the simplified expression is:

$36 + 9 \sqrt{3}$

Let me know if you'd like more details or further explanation.

Here are 5 related questions to expand on this:

1. What is the general rule for multiplying square roots with coefficients?
2. Can you factor out any terms from $36 + 9 \sqrt{3}$?
3. How would you approach simplifying an expression with higher powers of square roots?
4. What happens if you had a different base under the square root, like $\sqrt{5}$ instead of $\sqrt{3}$?
5. How would you solve the equation if this expression were equal to a value, like $36 + 9 \sqrt{3} = x$?

Tip: When simplifying expressions with square roots, always combine like terms and apply basic properties of square roots such as $\sqrt{a} \times \sqrt{a} = a$.