Nested floors

Algebra Level 3

Solve: \[ \sqrt{\lfloor \sqrt{8} \rfloor+\sqrt{\lfloor \sqrt{8} \rfloor+\sqrt{\lfloor \sqrt{8} \rfloor+\sqrt{\lfloor \sqrt{8} \rfloor+\sqrt{\lfloor \sqrt{8} \rfloor+{. . .}}}}}}\]

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