Question

How do you solve `x^2=7`?

Answer 1

`x = sqrt(7)" "` or `" "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 `(sqrt(7))^2 = 7`

The other solution is `-sqrt(7)` since `(-sqrt(7))^2 = (-1)^2*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 ]]