# Homework Help: A very quick stupid question about square roots of squares

1. Jun 13, 2012

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

If I see an expression like

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

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

2. Jun 13, 2012

### Fightfish

Re: A very quick stupid question

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)

3. Jun 13, 2012

### dimension10

Re: A very quick stupid question about the square root of a square

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

4. Jun 14, 2012

### HunterDX77M

Re: A very quick stupid question

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.

5. Jun 15, 2012

### Ratch

Re: A very quick stupid question

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

Ratch

6. Jun 15, 2012

### Staff: Mentor

Re: A very quick stupid question

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.

7. Jun 15, 2012

### Ratch

Re: A very quick stupid question

Mark44,

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

Ratch

8. Jun 15, 2012

### Staff: Mentor

Re: A very quick stupid question

That's not what you told the OP.

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.

9. Jun 15, 2012

### Ratch

Re: A very quick stupid question

Mark44,

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

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

Ratch

10. Jun 15, 2012

### Staff: Mentor

Re: A very quick stupid question

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

The OP's question:

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

Your verbatim response in post #5 (again):

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

11. Jun 15, 2012

### Ratch

Re: A very quick stupid question

Mark44,

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

Ratch