Final answer:
The value of √14 divided by √686 simplifies to 1/7 after factoring out √14, and no further simplification can present it in the form of a single square root. Thus, the answer is not listed among the options provided.
Step-by-step explanation:
To determine the value of √14 divided by √686, we can simplify the square roots and divide.
- Firstly, we notice that 14 is a factor of 686. Specifically, 686 divided by 14 equals 49, or 14*49=686.
- So, √686 can be written as √(14*49) which simplifies to √14 * √49.
- The square root of 49 is 7. So we have √14 divided by (√14 * 7).
- Dividing √14 by √14 gives 1, and we are left with 1/7.
- Since √14/√14 is 1, and 1/7 is simply 1/7, there's no additional simplification needed.
So, the final simplified form of √14 divided by √686 is 1/7, which correlates to √2 divided by √14. Therefore, none of the given options (a, b, c, d) are correct.