{{√ 2 } over {√ {(2 + √ 3 )} - √ {(2

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Gujarati

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Basic of Logarithms

easy

${{\sqrt 2 } \over {\sqrt {(2 + \sqrt 3 )} - \sqrt {(2 - \sqrt 3 } )}} = $

$0$

$1$

$\sqrt 2 $

$1/\sqrt 2 $

Solution

(b) ${{\sqrt 2 } \over {\sqrt {2 + \sqrt 3 } – \sqrt {2 – \sqrt 3 } }} = {{\sqrt 2 \,\left( {\sqrt {2 + \sqrt 3 } + \sqrt {2 – \sqrt 3 } } \right)} \over {(2 + \sqrt 3 ) – (2 – \sqrt 3 )}}$

$ = {{\sqrt {4 + 2\sqrt 3 } + \sqrt {4 – 2\sqrt 3 } } \over {2\sqrt 3 }} = {{(\sqrt 3 + 1)\, + \,(\sqrt 3 – 1)} \over {2\sqrt 3 }} = 1$.

Standard 11

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