Question

------------HOLA MATES ------------------

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Given
$\sqrt{2} = 1.414 \: and \: \sqrt{6} = 2.449. \\ find \: the \: value \: of \: \\ \frac{1}{ \sqrt{3} - \sqrt{2} - 1 } . \\ correct \: up \: to \: 3 \: decimal \: places$
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Answer 1

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Refer to the attachment for the solution.

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Answer 2

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Given,

$\sqrt{2} = 1.414 \: and \: \sqrt{6} = 2.499$


$\frac{1}{ \sqrt{3} - \sqrt{2} - 1 }$

$= \frac{1}{ \sqrt{3} - \sqrt{2} - 1} \times \frac{ \sqrt{3} - \sqrt{2} - 1 }{ \sqrt{3} - \sqrt{2} \times 1}$


$= \frac{ \sqrt{3 } + ( \sqrt{2} + 1)}{3 - {( \sqrt{2} + 1) }^{2} }$


$= \frac{ \sqrt{3} + \sqrt{2} + 1}{3 - 3 - \sqrt[2]{2} }$


$\frac{ \sqrt{3} + \sqrt{2} + 1 }{ \sqrt[2]{2} }$

$= \frac{( \sqrt{3} + \sqrt{2} + 1)}{ \sqrt[2]{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} }$

$= \frac{ \sqrt{3} + \sqrt{2} + \sqrt{2} }{ - 4}$

$= \frac{ - 1}{4} ( \sqrt{3} + \sqrt{2} + \sqrt{2} )$

$= \frac{ - 1}{4} (2.449 + 1 .414 + 2)$

$= \frac{ - 1}{4} (5.063)$

$= \frac{ - (5.063)}{4}$

$= - 1.466$


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