Question

Va rog frumos sa ma ajutati!
$Ordonati~crescator~numerele~si~explicati~cum~ati~facut:\\0,125;4- \sqrt{15} ; \sqrt{17} -4.$

Answer 1

$Comparam~numerele~0,125~si~4- \sqrt{15}. \\ \\ 0,125~?~4- \sqrt{15} ~~~~~~~| \cdot 8\\ \\ 1~?~32-8 \sqrt{15} \\ \\ 8 \sqrt{15}~?~31.~Ambii~membri~fiind~pozitivi,~putem~ridica~la~patrat, \\ \\ semnul~ramanand~nemodificat: \\ \\ 64 \cdot 15~?~31^2 \\ \\ 960~?~961,~dar~960\ \textless \ 961~\Rightarrow~0,125\ \textless \ 4- \sqrt{15}$

$Comparam~numerele~0,125~si~~ \sqrt{17}-4. \\ \\ 0,125~?~\sqrt{17}-4~~~~~~| \cdot 8 \\ \\ 1~?~8 \sqrt{17} -32 \\ \\ 33~?~8 \sqrt{17}.~Ambii~membri~fiind~pozitivi,~putem~ridica~la~patrat, \\ \\ semnul~ramanand~nemodificat:\\ \\ 33^2~?~64 \cdot 17 \\ \\ 1089~?~1088,~dar~1089\ \textgreater \ 1088 \Rightarrow 0,125\ \textgreater \ \sqrt{17}-4.$

$Deci~ \boxed{\sqrt{17}-4\ \textless \ 0,125\ \textless \ 4- \sqrt{15}}~.$