I have downloaded the NLCD 2011. It has different formats of files (i.e. .rrd, .ige). I tried to open the (.rrd) file using ArcGIS 10.5.1 but it couldn't open it.
Can you suggest me how can I view the land cover classes from here?
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The files you describe (.rrd, .ige) are not different formats but rather part of an Imagine (.img) raster format. In addition to the ige you will also need the .img file which is the actual raster.
The ige file is the index file for large rasters and was the solution to addressing these files in 32bit applications and operating systems, way back when. Paul Beaty has a brief description of the ige format on his blog.
The rrd (reduced resolution dataset) file is a pyramid file for faster display. ESRI has a good description of pyramid files in their online help.