Let's simplify the expression:
[tex]\begin{gathered} 4\sqrt[]{18}-2\sqrt[]{63}+\sqrt[]{175}+5\sqrt[]{98}=4\sqrt[]{9\cdot2}-2\sqrt[]{9\cdot7}+\sqrt[]{25\cdot7}+5\sqrt[]{49\cdot2} \\ =4\cdot3\sqrt[]{2}-2\cdot3\sqrt[]{7}+5\sqrt[]{7}+5\cdot7\sqrt[]{2} \\ =12\sqrt[]{2}-6\sqrt[]{7}+5\sqrt[]{7}+35\sqrt[]{2} \\ =47\sqrt[]{2}-\sqrt[]{7} \end{gathered}[/tex]Therefore the simplified form is:
[tex]47\sqrt[]{2}-\sqrt[]{7}[/tex]