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Problem #PRU-116430

Problems Algebra Surds. Rational powers Irrational inequalities.

Solve the following inequality: $x + y^{2} + \sqrt{x - y^{2} - 1} \leq 1$ .

Problem #PRU-65593

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

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