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
The square root of $\frac{(0.75)^3}{1-(0.75)}+\left[0.75+(0.75)^2+1\right]$ is
The rationalising factor of ${a^{1/3}} + {a^{ - 1/3}}$ is
If ${x^y} = {y^x},$then ${(x/y)^{(x/y)}} = {x^{(x/y) - k}},$ where $k = $
${{\sqrt {(5/2)} + \sqrt {(7 - 3\sqrt 5 )} } \over {\sqrt {(7/2)} + \sqrt {(16 - 5\sqrt 7 )} }}=$
If $x = \sqrt 7 + \sqrt 3 $ and $xy = 4,$then ${x^4} + {y^4}=$