If $5\sqrt{3}+\sqrt{243}=24.249$, then what will be the value of $\sqrt{192}+15\sqrt{3}$?

Given equation:
$$5\sqrt{3}+\sqrt{243}=24.249$$

First, simplify $\sqrt{243}$:

$$\sqrt{243}=\sqrt{81\times 3}=9\sqrt{3}$$

Substitute this back into the given equation:

$$5\sqrt{3}+9\sqrt{3}=24.249$$

$$14\sqrt{3}=24.249$$

$$\sqrt{3}=\frac{24.249}{14}$$

Now, we need to evaluate the expression: $\sqrt{192}+15\sqrt{3}$
Simplify $\sqrt{192}$:

$$\sqrt{192}=\sqrt{64\times 3}=8\sqrt{3}$$

Substitute this value into the target expression:

$$\text{Value}=8\sqrt{3}+15\sqrt{3}=23\sqrt{3}$$

Substitute the value of $\sqrt{3}$ from the first part:

$$\text{Value}=23\times \left(\frac{24.249}{14}\right)$$

$$\text{Value}=\frac{557.727}{14}\approx 39.8376$$

Rounding off to two decimal places, we get $39.84$.