Square roots + - sign deciding Is it correct to say that for solving x^2 = 49 , we can square root both sides we would get |x| = 7 so that means x can be either 7 or -7 ? If yes in the situation like finding square root of some numbers let say 100 taking square root of that will give +10 or -10 too ? +10 is only true because the (square root function ) gives always positive answer ? But when we are considering a variable x square root it can be both + - values because we dont know where √x might lie ?
 A: What you wrote is mostly correct, if a little confusingly written. The situation is as such:

*

*For every positive real number $a$, the equation $x^2=a$ has precisely two solutions.

*The two solutions of the equation $x^2=a$ have the same absolute value, but one of the solutions is positive and the other is negative. For example, the equation $x^2=100$ has two solutions, one solution is $10$, the other is $-10$.

*The square root is a function that maps non-negative real numbers to non-negative real numbers. It is defined such that $\sqrt{a}$ is defined as the non-negative solution to the equation $x^2=a$. Because of the properties above, this is a well defined function.


Taking all that I wrote into consideration, there are a few things you wrote that are not true. In particular:

In the situation like finding square root of some numbers let say 100 taking square root of that will give +10 or -10 too ?

No. The square root of $100$ is $10$. The number $-10$ is not equal to the number $\sqrt{100}$. However, both the number $10$ and the number $-10$ are solutions to the equation $x^2=100$.

But when we are considering a variable x square root it can be both + - values because we dont know where √x might lie

No. We know the square root of a positive number is always positive. However, when solving an equation like $x^2=a$, then, if all we know about $x$ is that it solves that equation, then we know that $x$ is equal to either $\sqrt{a}$ or it is equal to $-\sqrt{a}$.
