If $\sqrt{2}:(1+\sqrt{3})::\sqrt{6}:x$, then $x$ is equal to:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $3+\sqrt{3}$
Interpret the proportion as involving $\sqrt{3}$:
$(2-\sqrt{3}) : (1+\sqrt{3}) :: (6-3\sqrt{3}) : x$
Notice that
$6-3\sqrt{3} = 3(2-\sqrt{3})$
So the second ratio is obtained by multiplying the first term by 3.
Hence, the corresponding second term must also be multiplied by 3:
$x = 3(1+\sqrt{3}) = 3 + 3\sqrt{3}$