The number \( \sqrt{27 + \sqrt{200} } \) can be simplified to the form \( a + \sqrt{b}\), where \(a\) and \(b\) are positive integers. Find the product \(ab\).

**Details and assumptions**

This problem first appeared in Christoff Rudolff's book **Coss**, which is perhaps the first German algebra book. It was written in 1525. Rudoff was the first to use our notation for the square root.

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