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Problem #PRU-65593

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Algebra and arithmetic Surds. Rational powers. Irrational inequalities.

It is known that $a > 1$ . Is it always true that $⌊ \sqrt{⌊ \sqrt{a} ⌋} ⌋ = ⌊ \sqrt{4} a ⌋$ ?