# A Root of a Root

Algebra Level 2

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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