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).
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