import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem mathd_algebra_17
  (a : ℝ)
  (h₀ : Real.sqrt (4 + Real.sqrt (16 + 16 * a)) + Real.sqrt (1 + Real.sqrt (1 + a)) = 6) :
  a = 8 := by sorry