If $x = {{\sqrt 5 + \sqrt 2 } \over {\sqrt 5 - \sqrt 2 }},y = {{\sqrt 5 - \sqrt 2 } \over {\sqrt 5 + \sqrt 2 }},$ then $3{x^2} + 4xy - 3{y^2} = $
${1 \over 3}[56\sqrt {10} - 12]$
${1 \over 3}[56\sqrt {10} + 12]$
${1 \over 3}[56 + 12\sqrt {10} ]$
None of these
The rationalising factor of $2\sqrt 3 - \sqrt 7 $ is
If ${{{{({2^{n + 1}})}^m}({2^{2n}}){2^n}} \over {{{({2^{m + 1}})}^n}{2^{2m}}}} = 1,$ then $m =$
${{\sqrt {6 + 2\sqrt 3 + 2\sqrt 2 + 2\sqrt 6 } - 1} \over {\sqrt {5 + 2\sqrt 6 } }}$
The square root of $\frac{(0.75)^3}{1-(0.75)}+\left[0.75+(0.75)^2+1\right]$ is
The value of $\sqrt {[12 - \sqrt {(68 + 48\sqrt 2 )} ]} = $