To check if you have a correct connection to your SQL database without installing third pary tools you can take advantage of a standard SQL tool in Windows.
This is called : Microsoft Universal Data Link files with extension *.UDL.
It was designed to save and export SQL connections but it can easily be used for testing SQL connectivity.
Create a new text document and give it the *.udl extension, for example TestsqlDatabase.udl
After you saved the file, double click it, the Data link properties tab will open. Fill in you DB settings and your are able to test the connection.