The square root of $\sqrt {(50)} + \sqrt {(48)} $ is
${2^{1/4}}(3 + \sqrt 2 )$
${2^{1/4}}(\sqrt 3 + 2)$
${2^{1/4}}(2 + \sqrt 2 )$
${2^{1/4}}(\sqrt 3 + \sqrt 2 )$
If ${2^x} = {4^y} = {8^z}$ and $xyz = 288,$ then ${1 \over {2x}} + {1 \over {4y}} + {1 \over {8z}} = $
The rationalising factor of ${a^{1/3}} + {a^{ - 1/3}}$ is
${{{{[4 + \sqrt {(15)} ]}^{3/2}} + {{[4 - \sqrt {(15)} ]}^{3/2}}} \over {{{[6 + \sqrt {(35)} ]}^{3/2}} - {{[6 - \sqrt {(35)} ]}^{3/2}}}} = $
If $a = \sqrt {(21)} - \sqrt {(20)} $ and $b = \sqrt {(18)} - \sqrt {(17),} $ then
The value of ${{15} \over {\sqrt {10} + \sqrt {20} + \sqrt {40} - \sqrt 5 - \sqrt {80} }}$ is