# when simplified is

Question:

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

(a) positive and irrational

(b) positive and rational

(c) negative and irrational

(d) neqative and rational

Solution:

$(6+\sqrt{27})-(3+\sqrt{3})+(1-2 \sqrt{3})$

$=6+\sqrt{3 \times 3 \times 3}-(3+\sqrt{3})+(1-2 \sqrt{3})$

$=6+3 \sqrt{3}-3-\sqrt{3}+1-2 \sqrt{3}$

$=4$

Thus, the given expression when simplified is positive and rational.

Hence, the correct answer is option (b).