Suppose x=1. Sqrt(1^2) = 1.

Suppose x=0. sqrt(0^2) = 0

Suppose x=-1 sqrt(-1^2) = 1

So from this we can ascertain that sqrt(x^2) is equal to the SIZE of x (as in the modulus of x), or |x|

I hope this helps.

X is of the principle square root - the one we normally refer to when asking what a square root is. But the answer is plus or minus x, assuming we're talking real numbers. If x = 2 then obviously x^2 = 4, but the square root of 4 is always plus or minus 2. So both answers hold.

You could of course say that the answer is the absolute value of x, but it's simpler to refer to plus or minus (I don't know how to make the symbol!) - and shown nicely as a symmetrical parabola when plotting the curve y = x ^2.

The claim that sqrt{x^2} = x is false since -1 is a counterexample.

I am asking the question since too many students do not know the answer. ...

There is no need to substitute anything. This is basic elementary school pre-algebra. The square root of x^2 is always either x or -x. The answer 'x' is not wrong, just incomplete.

(If you know the answer already, why ask the question?)

Hint: Let y = sqrt{x^2}. Make a table of values. Substitute integers from -5 to 5 for x, then plot the points (x, y) on a graph. Connect the dots to form a graph.

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