Given the radical:
[tex]\sqrt[]{224}[/tex]Let's reduce the radical.
Factor out 16 from 224
[tex]\sqrt[]{16(14)}[/tex]Rewrite 16 as 4²:
[tex]\sqrt[]{4^2\ast14}[/tex][tex]4\sqrt[]{14}[/tex]Thererfore, the simplified radical is:
[tex]4\sqrt[]{14}[/tex]