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Đáp án+Giải thích các bước giải:

$a)$ Ta có:

$0,(3)=3.0,(1)=3.\dfrac{1}{9}=\dfrac{1}{3}$
$[0,(3)]^2=(\dfrac{1}{3})^2=\dfrac{1}{9}=0,(1)$

$(0,3)^2=0,09$

Do $0,(1)>0,09$

$⇒ [0,(3)]^2>(0,3)^2$

Vậy $[0,(3)]^2>(0,3)^2$

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$b)$ Ta có:

$\sqrt{215}>\sqrt{169}=13$

$⇒ \sqrt{215}>13$

Vậy $\sqrt{215}>13$

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$c)$ Ta có:

$\sqrt{72}>\sqrt{64}=8$

$⇒-\sqrt{72}<-8$

Vậy $-\sqrt{72}<-8$

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$d)$ Ta có:

$2\sqrt{3} = \sqrt{2^2.3}=\sqrt{12}$

$3\sqrt{2}=\sqrt{3^2.2}=\sqrt{18}$

Do $\sqrt{12}<\sqrt{18}$

$⇒ 2\sqrt{3}<3\sqrt{2}$

Vậy $2\sqrt{3}<3\sqrt{2}$

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