Toán 9 [ Thực hiện phép tính]

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transformers123

a/ $\sqrt{5}+\sqrt{9-4\sqrt{5}}$
$=\sqrt{5}+\sqrt{4-4\sqrt{5}+5}$
$=\sqrt{5}+\sqrt{(2-\sqrt{5})^2}$
$=\sqrt{5}+\sqrt{5}-2$
$=2\sqrt{5}-2$
 
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transformers123

b/ $\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}$

$=\dfrac{\sqrt{24-16\sqrt{3}}-\sqrt{48-24\sqrt{3}}}{\sqrt{2}}$

$=\dfrac{\sqrt{16-8\sqrt{12}+12}-\sqrt{36-12\sqrt{12}+12}}{\sqrt{2}}$

$=\dfrac{4-\sqrt{12}-6+\sqrt{12}}{\sqrt{2}}$

$=\dfrac{-2}{\sqrt{2}}$

$=-\sqrt{2}$
 
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transformers123

d/ $\sqrt{14+6\sqrt{5}}+\sqrt{14-6\sqrt{5}}$
$=\sqrt{9+6\sqrt{5}+5}+\sqrt{9-6\sqrt{5}+5}$
$=3+\sqrt{5}+3-\sqrt{5}$
$=6$
 
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toiyeu9a3

c. $\sqrt{4 - \sqrt{9 + 4\sqrt{2}}}$
$= \sqrt{4 - \sqrt{(2\sqrt{2} + 1)^2}}$
$= \sqrt{3 - 2\sqrt{2}}$
$=\sqrt{2} - 1$
 
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