Sears, Roebuck and Co. will open a "financial service center" in its Fair Oaks Mall store in July as part of a nationwide test of Sears' planned expansion into the real estate and stock brokerage businesses.

The Fairfax County unit is one of eight Sears stores that will get full-service, in-store branches of Coldwell Banker real estate and Dean Witter Reynolds securities, the two firms acquired last year by Sears.

Along with washing machines, tires and clothing, the test stores will sell stocks, mutual funds, bonds, Sears' new money market fund, real estate, mortgage insurance and all the conventional insurance policies already offered by Sears' Allstate subsidiary.

The announcement in Chicago of Sears' plans by Chairman Edward Telling came after months of speculation about how the nation's biggest retailer would expand into financial services.

"We are optimistic about the potential," Telling told a group of stock analysts. "If they are as successful as we expect them to be, we will be opening a network of financial service centers in Sears stores in 1983 and the years ahead."

The test will not mean that stock brokers or real estate salesmen will be sandwiched in between the appliance salesmen and auto service departments. Instead, the financial service centers will be set up in what Telling described as "a professional office atmosphere" in a 1,200-square-foot department carved out of the retail store.

In the Washington area, where Coldwell Banker and Dean Witter Reynolds are already well established in the real estate and investment business, the Sears "financial service center" will function as another branch of those companies.