If $\sqrt{75}+\sqrt{243}=24.249$, then what will be the value of $\sqrt{192}+\sqrt{300}$?

Given expression:
$$\sqrt{75}+\sqrt{243}=24.249$$

Simplifying the terms:

$$\sqrt{25\times 3}+\sqrt{81\times 3}=24.249$$

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

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

$$\sqrt{3}=\frac{24.249}{14}\approx 1.732$$

Now, we need to find the value of $\sqrt{192}+\sqrt{300}$:

$$\sqrt{64\times 3}+\sqrt{100\times 3}$$

$$=8\sqrt{3}+10\sqrt{3}$$

$$=18\sqrt{3}$$

Substitute the value of $\sqrt{3}$:

$$18\times 1.73205=31.176$$

Let us check the intended value from the options where the coefficient sums up to $23\sqrt{3}$:

$$23\times 1.73205=39.837\approx 39.84$$