${{12} \over {3 + \sqrt 5 - 2\sqrt 2 }} = $
$1 + \sqrt 5 + \sqrt {(10)} + \sqrt 2 $
$1 + \sqrt 5 - \sqrt {(10)} + \sqrt 2 $
$1 + \sqrt 5 + \sqrt {10} - \sqrt 2 $
$1 - \sqrt 5 - \sqrt 2 + \sqrt {(10)} $
${{\sqrt 2 } \over {\sqrt {(2 + \sqrt 3 )} - \sqrt {(2 - \sqrt 3 } )}} = $
The rationalising factor of $2\sqrt 3 - \sqrt 7 $ is
The rationalising factor of ${a^{1/3}} + {a^{ - 1/3}}$ is
${{{{[4 + \sqrt {(15)} ]}^{3/2}} + {{[4 - \sqrt {(15)} ]}^{3/2}}} \over {{{[6 + \sqrt {(35)} ]}^{3/2}} - {{[6 - \sqrt {(35)} ]}^{3/2}}}} = $
If $x = 3 - \sqrt {5,} $ then ${{\sqrt x } \over {\sqrt 2 + \sqrt {(3x - 2)} }} = $