how do i connect these objects to make a square?

Select them all and group them.

Apply the Effect > Convert to shape > Rectangle with 0 

Expand appearance

Reading the other answers -> this might not be the kind of square you want to have.

So much quicker just to draw a new square with rounded corners... (Rounded Rectangle Tool)

Endas, hi.

A super simple way would be draw out your rectangle, give it a Stoke weight with Round Cap and Round Join.

Then Object>Path>Outline.

Now you have Fills.

Same as your example all connected.

K

There are multiple ways to go about it.

You can use the Direct Selection tool to drag the anchor points on the ends of those dashes to overlap the white gaps. Use the shift key to constrain horizontal and vertical movement when dragging. Then use the Unite function in the Pathfinder palette to weld over the overlapping paths.

Another method: break apart that compound path (Object>Compound Path>Release) and/or Ungroup it. Sometimes both has to be done. Hold down the Shift and Alt/Option keys to drag new copies of the straight dashes to fill the gaps. Then use the Unite command to weld the objects.

Another approach (probably more time consuming): use the Direct Selection tool to select all the anchor points next to the gaps and then use the Cut command (scissors icon) to break open the paths. Ungroup the results. Delete the half circle path segments of those paths. Span the open line gaps by selecting the anchor points at each gap with the Direct Selection tool and using the Join command (Ctrl/Command+J).