If $R=(6\sqrt{6}+14{)}^{2n+1}$and $f=R-\left[R\right]$ , where $[ ]$ denotes the greatest integer function, then  $Rf$equals 

 

Let $G=(6\sqrt{6}-14{)}^{2n+1}$ . Then, 

$R-G=(6\sqrt{6}+14{)}^{2n+1}-(6\sqrt{6}-14{)}^{2n+1}$ 

$\Rightarrow R-G=2\left\{{ }^{2n+1}{C}_1\left(6\sqrt{6}{)}^{2n}\right(14)+\dots \right\}$

$\Rightarrow R-G=$An even integer 

$\Rightarrow \left[R\right]+f-G=$An even integer 

$\begin{array}{l}\Rightarrow f=G\\ \therefore Rf=RG=(6\sqrt{6}+14{)}^{2n+1}(6\sqrt{6}-14{)}^{2n+1}={20}^{2n+1}\end{array}$