Question

pls solve step by step try to do it in pAPER

Answer 1

Note: I don't have pen and paper with me. Sorry about that.

Answer: Option(D)

Explanation:


$Given : \frac{2( \sqrt{2} + \sqrt{6} ) }{3( \sqrt{2+ \sqrt{3} }) }$

On rationalizing, we get

$\frac{2( \sqrt{2} + \sqrt{6} ) }{3 (\sqrt{2 + \sqrt{3} }) } * \frac{ \sqrt{2 + \sqrt{3} } }{ \sqrt{2 + \sqrt{3} } }$

$\frac{2( \sqrt{2} + \sqrt{6})( \sqrt{2 + \sqrt{3} }) }{6 + 3 \sqrt{3} }$

On rationalising, we get

$\frac{2( \sqrt{2} + \sqrt{6})( \sqrt{2+ \sqrt{3} } )(6 - 3 \sqrt{3})}{(6 + 3 \sqrt{3})(6 - 3 \sqrt{3} ) }$

$\frac{6 \sqrt{6} \sqrt{2+ \sqrt{3} } - 6 \sqrt{2} \sqrt{2 + \sqrt{3} } }{36 - 27}$

$\frac{ \sqrt{6}( \sqrt{6} - \sqrt{2}) \sqrt{2 + \sqrt{3} } }{9}$

$\frac{2( \sqrt{6} - \sqrt{2} ) \sqrt{2 + \sqrt{3} } }{9}$

$\frac{2( \sqrt{6} - \sqrt{2} ) \sqrt{2 + \sqrt{3} } }{3}$

$\frac{2 \sqrt{2 + \sqrt{3} } * \sqrt{6} + 2 \sqrt{2 + \sqrt{3} } (- \sqrt{2}) }{3}$

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

$\frac{2 \sqrt{3} + 6 - 2 \sqrt{3} - 2 }{3}$

$\frac{4}{3}$



Hope this helps!

Answer 2

Hi,

Please see the attached file!


Thanks