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Found: 3

Problems Calculus Real numbers Rational and irrational numbers Algebra and arithmetic Surds. Rational powers. Square roots

12–16 2.0

Prove that the number $\sqrt{2} + \sqrt{3} + \sqrt{5} + \sqrt{7} + \sqrt{11} + \sqrt{13} + \sqrt{17}$ is irrational.

Problem #PRU-65593

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

12–14 3.0

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

Problem #PRU-66357

Problems Algebra and arithmetic Surds. Rational powers. Irrational inequalities.

13–13 2.0

It is known that $a = x + y + \sqrt{x y}$ , $b = y + z + \sqrt{y z}$ , $c = x + z + \sqrt{x z}$ . where $x > 0$ , $y > 0$ , $z > 0$ . Prove that $a + b + \sqrt{a b} > c$ .