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The square root of a negative number is known as an imaginary number. In this case, the square root of negative 37 would be represented as √(-37) = √37i, where "i" is the imaginary unit equal to the square root of -1. This means that the square root of negative 37 is the square root of 37 multiplied by the imaginary unit "i".
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TLDR: The solution is an irrational number number known as the square root of 37. This number is approximately equal to 6.0827625303. A method of arriving at the approximation: One way to arrive at this approximation is using Newton's method with the function x^2-37. To get a good first guess, consider that 37 is very close to a square number (36), whose square root is 6. So, you can use a first guess of 6 for Newton's method.
Buy a calculator with a square root button? Approximately 6.08276. Since the square root of 37 is an irrational number, its decimal representation neither terminates nor repeats. See http://en.wikipedia.org/wiki/Irrational_number.
Any number that is a multiple of 37 can be divided by 37 without leaving a remainder. In other words, any number that can be expressed as 37 multiplied by an integer (such as 37, 74, 111, etc.) is divisible by 37.