The value of $(6+\sqrt{27})-(3+\sqrt{3})+(1-2\sqrt{3})$ when simplified is :

The correct option is D (positive and rational)

Given $=6+\sqrt{27}-(3+\sqrt{3})+(1-2\sqrt{3})$
$=6+3\sqrt{3}-3-\sqrt{3}+1-2\sqrt{3}$
Groping the square root terms,
$=3\sqrt{3}-\sqrt{3}-2\sqrt{2}+6-3+1$
$=3\sqrt{3}-3\sqrt{3}+7-3$
$=4$
$4$ is a positive rational number
Hence, correct answer is option C.