12. 比较下列各组数的大小:
(1) $ \sqrt[3]{1 1} $与2; (2) $ \frac{8}{3} $与 $ \sqrt[3]{2 0} $; (3)-4, $ -\sqrt{1 5},-\sqrt[3]{1 0 0}. $
(1) $ \sqrt[3]{1 1} $与2; (2) $ \frac{8}{3} $与 $ \sqrt[3]{2 0} $; (3)-4, $ -\sqrt{1 5},-\sqrt[3]{1 0 0}. $
答案
12.解:(1)$\because11>8$,
$\therefore\sqrt[3]{11}>\sqrt[3]{8}$.
$\therefore\sqrt[3]{11}>2$.
(2)$\because\dfrac{512}{27}<20$,
$\therefore\sqrt[3]{\dfrac{512}{27}}<\sqrt[3]{20}$.
$\therefore\dfrac{8}{3}<\sqrt[3]{20}$.
(3)$\because16>15$,
$\therefore\sqrt{16}>\sqrt{15}$.
$\therefore4>\sqrt{15}$.
$\therefore-4<-\sqrt{15}$.
$\because64<100$,
$\therefore\sqrt[3]{64}<\sqrt[3]{100}$.
$\therefore4<\sqrt[3]{100}$.
$\therefore-4>-\sqrt[3]{100}$.
$\therefore-\sqrt[3]{100}<-4<-\sqrt{15}$.
$\therefore\sqrt[3]{11}>\sqrt[3]{8}$.
$\therefore\sqrt[3]{11}>2$.
(2)$\because\dfrac{512}{27}<20$,
$\therefore\sqrt[3]{\dfrac{512}{27}}<\sqrt[3]{20}$.
$\therefore\dfrac{8}{3}<\sqrt[3]{20}$.
(3)$\because16>15$,
$\therefore\sqrt{16}>\sqrt{15}$.
$\therefore4>\sqrt{15}$.
$\therefore-4<-\sqrt{15}$.
$\because64<100$,
$\therefore\sqrt[3]{64}<\sqrt[3]{100}$.
$\therefore4<\sqrt[3]{100}$.
$\therefore-4>-\sqrt[3]{100}$.
$\therefore-\sqrt[3]{100}<-4<-\sqrt{15}$.
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