Question

Сравните sqrt(2)+sqrt(3) и pi

Answer 1

$1<\sqrt2<2\; \; ,\; \; \; 1<\sqrt3<2\\\\1+1<\sqrt2+\sqrt3<2+2\; \; \to \; \; 2<\sqrt2+\sqrt3<4\\\\3<\pi <4\; \; ,\; \; \pi \approx 3,14159\\\\a)\; \; \sqrt2\approx 1,41421\; \; ,\; \; \sqrt3\approx 1,73205\; \; ,\; \; \sqrt2+\sqrt3\approx 3,14626\\\\\underline {\sqrt2+\sqrt3>\pi}$

$b)\; \; \sqrt2+\sqrt3\; \vee \pi \\\\(\sqrt2+\sqrt3)^2\; \vee\pi ^2\\\\2+2\sqrt6+3\; \vee \pi ^2\\\\5+2\sqrt6\; \vee \pi ^2\\\\5+2\cdot 2,449\; \vee \, 3,14^2\\\\9,898>9,8596\; \; \; \Rightarrow \; \; (\sqrt2+\sqrt3^2>\pi ^2\; \; \Rightarrow \; \; \underline {\sqrt2+\sqrt3>\pi }$