The rationalising factor of ${a^{1/3}} + {a^{ - 1/3}}$ is
${a^{1/3}} - {a^{ - 1/3}}$
${a^{2/3}} + {a^{ - 2/3}}$
${a^{2/3}} - {a^{ - 2/3}}$
${a^{2/3}} + {a^{ - 2/3}} - 1$
${{{{[4 + \sqrt {(15)} ]}^{3/2}} + {{[4 - \sqrt {(15)} ]}^{3/2}}} \over {{{[6 + \sqrt {(35)} ]}^{3/2}} - {{[6 - \sqrt {(35)} ]}^{3/2}}}} = $
${({x^5})^{1/3}}{(16{x^3})^{2/3}}$${\left( {{1 \over 4}{x^{4/9}}} \right)^{ - 3/2}} = $
If $x = \sqrt 7 + \sqrt 3 $ and $xy = 4,$then ${x^4} + {y^4}=$
The cube root of $9\sqrt 3 + 11\sqrt 2 $ is
The value of ${{15} \over {\sqrt {10} + \sqrt {20} + \sqrt {40} - \sqrt 5 - \sqrt {80} }}$ is