use binary search to narrow down the search space and keep multiplying the answer in each iteration by itself to check if it is equal to the double given. If it is lesser, move up the lower bound, else move down the upper bound.

There's a variation of the problem which says "find the square root of a double up to the third decimal digit". I'd just multiply the original number by 10^position (meaning, for 3 digit accuracy it'd be 10^3) and ran a simple loop to find the closest integer. As soon as i*i > 10^position * number, you can return (i-1)/10^position. It's hella slow and unimaginative, but it works and you won't sound like you knew this problem ahead of time (if you come up with a Babylonian solution).

Is it too obvious to ask if you can do double^.5 ?

I would respond by showing that I am thinking about the problem as it is defined, not by making assumtions about what is implied. This can result in product that does not meet the requirement specifications, which can be very costly: "What do you mean, a program or a function? A program would require input and output mechanisms to make it meaningful, but makes it pretty usesless as a job assessment question. A function makes more sense in this context. "