Answer: Yes, this is a reasonable estimation.
Explanation:
Number of badges in 1 box = 22
Therefore the total number of badges in 34 boxes= 34 times badges in 1 box

When we round off the total number of badges to the nearest hundreds, we get 748≈700 [as 748 is near to 700 than 800]
Estimated number of badges in 34 boxes=700
Therefore, Yes, this is a reasonable estimation.