The rationalising factor of $2\sqrt 3 - \sqrt 7 $ is
$\sqrt 3 + \sqrt 7 $
$2\sqrt 3 + \sqrt 7 $
$\sqrt 3 + 2\sqrt 7 $
None of these
If ${a^{x - 1}} = bc,{b^{y - 1}} = ca,{c^{z - 1}} = ab,$then $\sum {(1/x) = } $
$\root 4 \of {(17 + 12\sqrt 2 )} = $
If ${2^x} = {4^y} = {8^z}$ and $xyz = 288,$ then ${1 \over {2x}} + {1 \over {4y}} + {1 \over {8z}} = $
The value of $\sqrt {[12 - \sqrt {(68 + 48\sqrt 2 )} ]} = $
The rationalising factor of ${a^{1/3}} + {a^{ - 1/3}}$ is