Windows 10 comes with a search icon (a magnifying glass) in the taskbar. If you don't use that (as you can search by clicking on the Windows (Start Menu) icon), you can get rid of it as follows:
- Right-click on a free spot in the taskbar.
- Hover over "Cortana" and the click "Hidden".
- That's it.
If you have disabled Cortana, the menu sequence is "Search" > "Hidden".