A very quick stupid question about square roots of squares

[help1please]

If I see an expression like

$$\sqrt{E^2c^2}$$

I can just remove the square root sign right and replace it with Ec?

 

[Fightfish]

In general, no.

One must recall that the square root function always returns a positive value. So,
$$\sqrt{X^{2}} = |X|$$
This is aptly illustrated by $\sqrt{(-1)^{2}} = |-1| = 1$.
$\sqrt{X^{2}} = X$ iff X is positive.

(for simplicity, assume that X is always real)

 

[dimension10]

If I see an expression like

$$\sqrt{E^2c^2}$$

I can just remove the square root sign right and replace it with Ec?

You can't. And please improve the title a bit, like the one you see in the title of this post.

 

[member 422733]

In general, you cannot do that. If however, if you know for certain that E and c are both real and positive numbers, then yes you can simplify it to just Ec.

 

[Ratch]

help1please,

I can just remove the square root sign right and replace it with Ec?

I would say yes you can. Once a expression is squared, it loses its signed identity.

Ratch

 

[Mark44]

help1please,

I would say yes you can. Once a expression is squared, it loses its signed identity.

That is incorrect. Here's an example why.

$$ \sqrt{(-4)^2} \neq -4$$

IOW, if you square a negative number, and then take the square root, you don't get the negative number back.

 

[Ratch]

Mark44,

IOW, if you square a negative number, and then take the square root, you don't get the negative number back.

Correct, that is what I am averring. I am saying it loses its sign identity after it is squared.

Ratch

 

[Mark44]

Mark44,
Correct, that is what I am averring. I am saying it loses its sign identity after it is squared.

That's not what you told the OP.

I can just remove the square root sign right and replace it with Ec?

I would say yes you can. Once a expression is squared, it loses its signed identity.

So what you are telling the OP is that
$$ \sqrt{E^2c^2} = Ec$$

And that is true only if both E and c are nonnegative. If either is negative, the above is not true.

 

[Ratch]

Mark44,

Re: A very quick stupid question

--------------------------------------------------------------------------------

Originally Posted by Ratch
Mark44,
Correct, that is what I am averring. I am saying it loses its sign identity after it is squared.

That's not what you told the OP.

That is exactly what I told the OP. See post #5.

So what you are telling the OP is that

No, I am saying that √(E^2*C^2) = |E*C|

Ratch

 

[Mark44]

Mark44,
That is exactly what I told the OP. See post #5.

Yes, I saw post #5, and that is what I'm objecting to.

The OP's question:

I can just remove the square root sign right and replace it with Ec?

IOW, help1please is asking if $\sqrt{E^2c^2} = Ec$

Your verbatim response in post #5 (again):

I would say yes you can. Once a expression is squared, it loses its signed identity.

No, I am saying that √(E^2*C^2) = |E*C|

Well, I agree with that, but that isn't what you said before. Your previous response had no mention of absolute values.

 

[Ratch]

Mark44,

OK, you are right. I only half explained it.

Ratch