Factor $450=15^{2}\times 2$. Rewrite the square root of the product $\sqrt{15^{2}\times 2}$ as the product of square roots $\sqrt{15^{2}}\sqrt{2}$. Take the square root of $15^{2}$.
$$15\sqrt{2}+\sqrt{12}-\sqrt{48}-\sqrt{98}$$
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 $2^{2}$.
$$15\sqrt{2}+2\sqrt{3}-\sqrt{48}-\sqrt{98}$$
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 $4^{2}$.
$$15\sqrt{2}+2\sqrt{3}-4\sqrt{3}-\sqrt{98}$$
Combine $2\sqrt{3}$ and $-4\sqrt{3}$ to get $-2\sqrt{3}$.
$$15\sqrt{2}-2\sqrt{3}-\sqrt{98}$$
Factor $98=7^{2}\times 2$. Rewrite the square root of the product $\sqrt{7^{2}\times 2}$ as the product of square roots $\sqrt{7^{2}}\sqrt{2}$. Take the square root of $7^{2}$.
$$15\sqrt{2}-2\sqrt{3}-7\sqrt{2}$$
Combine $15\sqrt{2}$ and $-7\sqrt{2}$ to get $8\sqrt{2}$.
