Factor $12=2^{2}\times 3$. Rewrite the square root of the product $\sqrt{2^{2}\times 3}$ as the product of square roots $\sqrt{2^{2}}\sqrt{3}$. Take the square root of $2^{2}$.
$$2\sqrt{3}+\sqrt{75}$$
Factor $75=5^{2}\times 3$. Rewrite the square root of the product $\sqrt{5^{2}\times 3}$ as the product of square roots $\sqrt{5^{2}}\sqrt{3}$. Take the square root of $5^{2}$.
$$2\sqrt{3}+5\sqrt{3}$$
Combine $2\sqrt{3}$ and $5\sqrt{3}$ to get $7\sqrt{3}$.
