The cube root of $9\sqrt 3 + 11\sqrt 2 $ is
$2\sqrt 3 + \sqrt 2 $
$\sqrt 3 + 2\sqrt 2 $
$3\sqrt 3 + \sqrt 2 $
$\sqrt 3 + \sqrt 2 $
${4 \over {1 + \sqrt 2 - \sqrt 3 }} = $
The value of ${{15} \over {\sqrt {10} + \sqrt {20} + \sqrt {40} - \sqrt 5 - \sqrt {80} }}$ is
${{12} \over {3 + \sqrt 5 - 2\sqrt 2 }} = $
If $x + \sqrt {({x^2} + 1)} = a,$ then $x =$
If ${a^x} = {b^y} = {(ab)^{xy}},$ then $x + y = $