Problem $3$: A soil has $PL=30$ and $LL=80.$ Compute its plasticity index, and then describe the probable clay content $($i$.$e$.,$ small, moderate, or high$).$ Also, describe the soil based on the following table.

$\backslash$table$[[$Plasticity Index, IP$,$Classification,Dry Strength,$\backslash$table$[[$Visual$-$Manual Identification$],[$of Dry Sample$]],],[0-3,$Nonplastic,Very low,Falls apart casily,$9],[3-15,$Slightly plastic,Slight,Easily crushed with fingers,$\backslash$table$[[\sqrt[\phantom{2}]{8}$