Factor $45=3^{2}\times 5$. Rewrite the square root of the product $\sqrt{3^{2}\times 5}$ as the product of square roots $\sqrt{3^{2}}\sqrt{5}$. Take the square root of $3^{2}$.
$$\frac{7}{3\sqrt{5}}+\sqrt{300}-3\sqrt{48}$$
Rationalize the denominator of $\frac{7}{3\sqrt{5}}$ by multiplying numerator and denominator by $\sqrt{5}$.
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 $10^{2}$.
$$\frac{7\sqrt{5}}{15}+10\sqrt{3}-3\sqrt{48}$$
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 $4^{2}$.
