Factor $300=10^{2}\times 3$. Rewrite the square root of the product $\sqrt{10^{2}\times 3}$ as the product of square roots $\sqrt{10^{2}}\sqrt{3}$. Take the square root of $10^{2}$.
$$10\sqrt{3}+\sqrt{48}-\sqrt{147}$$
Factor $48=4^{2}\times 3$. Rewrite the square root of the product $\sqrt{4^{2}\times 3}$ as the product of square roots $\sqrt{4^{2}}\sqrt{3}$. Take the square root of $4^{2}$.
$$10\sqrt{3}+4\sqrt{3}-\sqrt{147}$$
Combine $10\sqrt{3}$ and $4\sqrt{3}$ to get $14\sqrt{3}$.
$$14\sqrt{3}-\sqrt{147}$$
Factor $147=7^{2}\times 3$. Rewrite the square root of the product $\sqrt{7^{2}\times 3}$ as the product of square roots $\sqrt{7^{2}}\sqrt{3}$. Take the square root of $7^{2}$.
$$14\sqrt{3}-7\sqrt{3}$$
Combine $14\sqrt{3}$ and $-7\sqrt{3}$ to get $7\sqrt{3}$.
