To solve this expression, we need to follow the order of operations (PEMDAS) and simplify each part step by step:

1. First, we simplify the expression inside the parentheses:

3:3√2 = 1√2

2. Next, we simplify the multiplication and division from left to right:

5×3 = 15
9×3√1 = 27√1 = 27
5×3√2 = 15√2
15√2÷4 = 3.75√2
3√3×1√2 = 3√6

3. Then, we add and subtract from left to right:

15 + 27 + 3√6 + 3.75√2

4. Finally, we simplify the percentage:

9÷2℅ = 0.09

5. Putting it all together, we get:

15 + 27 + 3√6 + 3.75√2 + 0.09

= 42 + 3√6 + 3.75√2 + 0.09

= 42.09 + 3√6 + 3.75√2

Therefore, 5×3+9×3√1+5×3√2÷4+3√3×3:3√2 ×9÷2℅ = 42.09 + 3√6 + 3.75√2.