# 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.