<s>[INST] Do you write plus/minus if a variable squares equals the square root of a number? For example, if I have $x^2 = \sqrt{49}$. I know that $7$ is the number, but as my final answer, do I write that $x = +\sqrt{7}$ and $-\sqrt{7}$ or just $x = \sqrt{7}$?
 [/INST] It depends on which field you expect/require the answer to be in:
If the answer is allowed to be a complex number, then the equation $x^2 = \sqrt{49}$ can be rewritten as $x^2 = 7$ OR $x^2 = -7$, which collectively yield four values: $x = +\sqrt{7}$, $x = -\sqrt{7}$, $x = +i\sqrt{7}$, and $x = -i\sqrt{7}$.
If the answer is required to be a real number, then the equation $x^2 = \sqrt{49}$ can be rewritten as $x^2 = 7$ OR $x^2 = -7$, which, since $x^2 = -7$ has no real solution, yields only two values: $x = +\sqrt{7}$ and $x = -\sqrt{7}$.
If the answer is required to be a rational number, or a number in an extension of the rationals which does not contain $\sqrt{7}$, then of course there is no solution.
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