${{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)} $
${4 \over {1 + \sqrt 2 - \sqrt 3 }} = $
${{{{[4 + \sqrt {(15)} ]}^{3/2}} + {{[4 - \sqrt {(15)} ]}^{3/2}}} \over {{{[6 + \sqrt {(35)} ]}^{3/2}} - {{[6 - \sqrt {(35)} ]}^{3/2}}}} = $
Let ${7 \over {{2^{1/2}} + {2^{1/4}} + 1}}$$ = A + B{.2^{1/4}} + C{.2^{1/2}} + D{.2^{3/4}}$, then $A+B+C+D= . . .$
If ${a^x} = {(x + y + z)^y},{a^y} = {(x + y + z)^z}$, ${a^z} = {(x + y + z)^x},$ then
${{\sqrt {6 + 2\sqrt 3 + 2\sqrt 2 + 2\sqrt 6 } - 1} \over {\sqrt {5 + 2\sqrt 6 } }}$