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 $2^{2}$.
$$1\times 2\sqrt{3}\sqrt{138}$$
Multiply $1$ and $2$ to get $2$.
$$2\sqrt{3}\sqrt{138}$$
Factor $138=3\times 46$. Rewrite the square root of the product $\sqrt{3\times 46}$ as the product of square roots $\sqrt{3}\sqrt{46}$.
