# Nested Square Roots

Algebra Level 5

If $\sqrt{4+\sqrt{4-\sqrt{4+\sqrt{4-\cdots}}}}=\frac{a+\sqrt{b}}{c}$ such that the fraction in the RHS cannot be simplified any further and $$b$$ is square free and $$a,b,c$$ are all integers, what is the value of $$a + b + c$$?

Extra Credit: Post a solution that can do it by hand without the requirement of quartic formula.

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