√10 <?> ³√29
This is a hard one. First, cube both sides.

√10 x √10 x √10 <?> 29
10√10 <?> 29

Now, square both sides.
100 x 10 <?> 29²
1000 <?> 29²
Don't be foolish enough to multiply out 29². We know 29² < 30² = 900 < 1000, so without calculating 29², we know it must be less than 1000.

The inequality is open to the left, and the original statement is TRUE.