${{3\sqrt 2 } \over {\sqrt 6 + \sqrt 3 }} - {{4\sqrt 3 } \over {\sqrt 6 + \sqrt 2 }} + {{\sqrt 6 } \over {\sqrt 3 + \sqrt 2 }} = $

Solution of the equation  ${4.9^{x - 1}} = 3\sqrt {({2^{2x + 1}})} $ has the solution

The rationalising factor of $2\sqrt 3 - \sqrt 7 $ is

If ${2^x} = {4^y} = {8^z}$ and $xyz = 288,$ then ${1 \over {2x}} + {1 \over {4y}} + {1 \over {8z}} = $

$\sqrt {(3 + \sqrt 5 )} - \sqrt {(2 + \sqrt 3 )} = $

The greatest number among $\root 3 \of 9 ,\root 4 \of {11} ,\root 6 \of {17}  $ is