${4 \over {1 + \sqrt 2 - \sqrt 3 }} = $
$2 + \sqrt 2 + \sqrt 6 $
$1 + \sqrt 2 + \sqrt 3 $
$3 + \sqrt 2 + \sqrt 3 $
None of these
The rationalising factor of ${a^{1/3}} + {a^{ - 1/3}}$ is
If ${a^{x - 1}} = bc,{b^{y - 1}} = ca,{c^{z - 1}} = ab,$then $\sum {(1/x) = } $
If $x = {{\sqrt 5 + \sqrt 2 } \over {\sqrt 5 - \sqrt 2 }},y = {{\sqrt 5 - \sqrt 2 } \over {\sqrt 5 + \sqrt 2 }},$ then $3{x^2} + 4xy - 3{y^2} = $
The square root of $\sqrt {(50)} + \sqrt {(48)} $ is
The value of ${{15} \over {\sqrt {10} + \sqrt {20} + \sqrt {40} - \sqrt 5 - \sqrt {80} }}$ is