# How do you solve x^2=7?

Jan 17, 2017

$x = \sqrt{7} \text{ }$ or $\text{ } x = - \sqrt{7}$

#### Explanation:

By definition, a square root of $7$ is a number which when squared gives $7$.

So one solution is $x = \sqrt{7}$ (the positive square root of $7$) since ${\left(\sqrt{7}\right)}^{2} = 7$

The other solution is $- \sqrt{7}$ since ${\left(- \sqrt{7}\right)}^{2} = {\left(- 1\right)}^{2} \cdot 7 = 7$

Any non-zero number has exactly $2$ square roots. If the original number is negative then those square roots are so called imaginary numbers.

[[ The term imaginary is rather unfortunate as such numbers are just as 'real' as Real numbers ]]