What does x equal if x square equals -3?

Answer 1

If you want to work with real numbers, there is no answer. the square of any number, whether positive or negative, is a positive number, so x2 cannot be -3.

If you accept complex numbers as a solution, the square root of minus 1 is called i (when squared, both i and -i give -1); the square root of -3 is equal to the square root of 3 times i, the square root of -4 is 2i, etc.

Complex numbers are frequently used in some areas of science (electricity, quantum mechanics, and others); in other areas, it just doesn't make sense to use them. Similarly, for some problems fractional solutions, or negative solutions, may be acceptable, for others, not.

Answer 2

If x squared equals -3, then x must equal the square root of -3. The square root of -3 is a complex number, specifically √(-3) = √3i, where i is the imaginary unit (√-1). Therefore, x equals ±√3i.