Final answer:
To simplify the expression √-12/√6, rewrite the square root of -12 as √(-1) * √12 and simplify the square roots separately. Then simplify the denominator by multiplying the square root of 6 by itself. Finally, combine the simplified numerator and denominator to get the answer.
Step-by-step explanation:
To simplify the expression √-12/√6, we can start by simplifying the square roots separately. The square root of -12 can be written as √(-1) * √12. Since the square root of -1 is represented as 'i' and the square root of 12 can be simplified to 2√3, the expression becomes i * 2√3 / √6.
Next, we can simplify the denominator by multiplying the square root of 6 by itself, resulting in 6.
Combining the simplified numerator and denominator, we have i * 2√3 / √6 = 2i√3 / 6 = √3 / 3 = Option C. 1/√2.