SOLUTION: Is sqrt(x^2) = x for every real number x? Please explain your reasoning.

Question 356824: Is sqrt(x^2) = x for every real number x? Please explain your reasoning.
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
Is sqrt(x^2) = x for every real number x? Please explain your reasoning.

x = -3, x^2 = 9, sqrt(x^2) = 3 or -3 since both squared equal 9
x = 0, x^2 = 0, sqrt(x^2) = 0, 0 is not positive or negative
x = 3, x^2 = 9, sqrt(x^2) = 3 or -3 since both squared equal 9

the principal square root is the positive root not the negative one

if you only looking for principal square roots, sqrt(x^2) = x is a one square to one root relationship

if you not just looking for principal square roots, sqrt(x^2) = x is a one square to two roots relationship

sqrt(x^2) = x, unless you looking for principal values of x has two values of x that will make the equation work, the positive value and the negative value, unless x = 0

So does sqrt(x^2) = x for every real number x?
Yes if x is the principal root of x^2.

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