Question

Aratati ca numarul p este natural , unde :

p= (2/√7+√5 + 3/√5-√2 ) *2

Rapid va rog !!!

Answer 1

$p=(\dfrac{2}{\sqrt{7} } + \sqrt{5}+\dfrac{3}{\sqrt{5} } - \sqrt{2})\cdot2=(\dfrac{2\sqrt{7} }{7}+\sqrt{5}+\dfrac{3\sqrt{5} }{5}-\sqrt2)\cdot2=(\dfrac{2\sqrt7}{7}+\dfrac{5\sqrt{5} + 3\sqrt{5} }{5}-\sqrt{2})\cdot2=(\dfrac{2\sqrt{7} }{7}+\dfrac{8\sqrt{5} }{5}-\sqrt{2})\cdot2=\dfrac{4\sqrt{7} }{7}+\dfrac{16\sqrt{5} }{5}-2\sqrt{2}$

$(=5,83885)$