**Core Concept**
The eradication of Helicobacter pylori (H. pylori) infection is crucial for the treatment of peptic ulcer disease and gastric malignancies. The ideal test for determining eradication should be sensitive, specific, and non-invasive.

**Why the Correct Answer is Right**
The correct answer is the urea breath test (UBT). The UBT detects the presence of H. pylori by measuring the carbon dioxide produced from the breakdown of urea by the bacterial enzyme urease. This test is based on the principle that H. pylori produces urease, which hydrolyzes urea into carbon dioxide and ammonia. The increased levels of carbon dioxide in the breath sample indicate the presence of H. pylori. The UBT is a non-invasive test that is well-tolerated and has high sensitivity and specificity for detecting H. pylori infection.

**Why Each Wrong Option is Incorrect**
**Option A:** Serum H. pylori IgG antibodies are not a good indicator of eradication, as they can remain positive for several months after successful treatment.
**Option B:** Gastric biopsy with histological examination is an invasive procedure that is not necessary for routine follow-up of H. pylori eradication.
**Option C:** Endoscopy with rapid urease test (RUT) is a more invasive procedure than the UBT and is not typically used for follow-up of H. pylori eradication.

**Clinical Pearl / High-Yield Fact**
The urea breath test (UBT) is a non-invasive and reliable method for detecting H. pylori infection and monitoring eradication. It is essential to perform the UBT at least 4-6 weeks after completing treatment to ensure that the antibiotic regimen has been effective.

**Correct Answer:** C. Rapid Urea Breath Test.