What is the square root of x^2?

[Hurkyl]

I think you might mean

$${ x }^{ 2 }=4\\ \sqrt{{ x }^{ 2 }}=\sqrt { 4 } \\ |x| = 2 \\ x=\pm 2$$

As a reminder for the OP, while this argument does prove

If x² = 4, then x = 2 or x = -2​

it does not prove

x = 2 and x = -2 are both solutions to x² = 4​

unless you can argue that every step is reversible. (they are in this case)

 

[tahayassen]

As a reminder for the OP, while this argument does prove

If x² = 4, then x = 2 or x = -2​

it does not prove

x = 2 and x = -2 are both solutions to x² = 4​

unless you can argue that every step is reversible. (they are in this case)

What do you mean by every step is reversible? Can you give me an example where they are not reversible?

 

[Mark44]

x = -2 $\Rightarrow$ x² = 4

The steps here are not reversible. If x² = 4, it does not necessarily imply that x = -2.

 

[Dalek1099]

As a reminder for the OP, while this argument does prove

If x² = 4, then x = 2 or x = -2​

it does not prove

x = 2 and x = -2 are both solutions to x² = 4​

unless you can argue that every step is reversible. (they are in this case)

Wrong.Is x=2 a solution to x^2=4?-yes and is x=-2 a solution to x^2=4-yes, they are both solutions.Saying x=two values simultaneously is wrong, which I think is what you meant and thinking about this, with everything said generally being correct in this thread about(x^0.5)^2 being= to + or-(x) or abs(x) this means that (x^a)^b doesn't always equal x^(ab), which is an exponentiation law-I suppose there always are exceptions.The steps are irreversible because the inverse has more than one image, which isn't right.

 

[micromass]

Wrong.Is x=2 a solution to x^2=4?-yes and is x=-2 a solution to x^2=4-yes, they are both solutions.Saying x=two values simultaneously is wrong, which I think is what you meant and thinking about this, with everything said generally being correct in this thread about(x^0.5)^2 being= to + or-(x) or abs(x) this means that (x^a)^b doesn't always equal x^(ab), which is an exponentiation law-I suppose there always are exceptions.The steps are irreversible because the inverse has more than one image, which isn't right.

What Hurkyl said was absolutely correct. I think you misinterpreted his post.

 

[tahayassen]

Alright, thanks for the help guys.