10. $[x]$ represents the greatest integer not exceeding $x$, $\{x\}$ represents the fractional part of $x$. Let $[\sqrt{27-10 \sqrt{2}}]=a$, $\{\sqrt{27-10 \sqrt{2}}\}=b$, then $a+b+\frac{2}{b}=$ $\qquad$ .
$7$