No. Republics are representative in some form by nature. To use the term "representative republic" is just redundant. While it was used in the past by at least one of the founding fathers of the United States of America, it actually doesn't mean any more than just saying "republic". It might or might not be considered proper English, but even if proper it is still unnecessarily redundant.
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Many military dictatorships are republics and do not have representative government.