OpenStudy (anonymous):

help on square roots and The little sign thingy that is confusing me

4 years ago
OpenStudy (anonymous):

help |dw:1377211229907:dw|

4 years ago
OpenStudy (tkhunny):

Well, that little sign thingy means at least 5 different things, so small wonder you find it confusing. It depends heavily on the context exactly what it means. What problem are you working on?

4 years ago
OpenStudy (anonymous):

a number that produces a specified quantity when multiplied by itself. "7 is a square root of 49"

4 years ago
OpenStudy (anonymous):

Well what I am having trouble with is what the + over minus means? how you do you square a negative is it the same as a positive?

4 years ago
OpenStudy (anonymous):

i know how to square so

4 years ago
OpenStudy (tkhunny):

You didn't answer my question. Depending on exactly what you are doing, it might mean different things.

4 years ago
OpenStudy (anonymous):

Yes it is. so the square root of -64 is -8

4 years ago
OpenStudy (debbieg):

"to square" a number simply means to multiply it by itself. $$\large 2^2=2\cdot2=4$$ $$\large x^2=x\cdot x$$

4 years ago
OpenStudy (debbieg):

Noooooo.... the square root of -64 is not defined in the real numbers!

4 years ago
OpenStudy (tkhunny):

No, the square root of -64 is NOT -8. (-8)^2 = +64

4 years ago
OpenStudy (debbieg):

$$\large (-8)^2=(-8)\cdot(-8)=64$$

4 years ago
OpenStudy (debbieg):

Squaring is just multiplying. So just as with any multiplying, positive x positive = positive negative x positive = negative negative x negative = positive

4 years ago
OpenStudy (anonymous):

@DebbieG , could you help me with a question? Just to make sure I am right.

4 years ago
OpenStudy (debbieg):

But back to the square root and the plus/minus symbol.... The square root is the number that you "square" to get the number under the symbol. So $$\large \sqrt{16}=\sqrt{4\cdot4}=4$$ Now notice, it is also true that $$\large (-4)\cdot(-4)=16$$. But here's the thing: we have DEFINED the square root operation to MEAN the POSITIVE number that, when multiplied by itself, gives you the number under the the sq root symbol, see what I mean?

4 years ago
OpenStudy (debbieg):

4 years ago
OpenStudy (debbieg):

So even though both $$\large 4\cdot4=16$$ and $$\large (-4)\cdot(-4)=16$$, only one of the two (that is, only one of 4 or -4) is DEFINED as the SQUARE ROOT of 16. That is: $$\large \sqrt{16}=4$$ But... $$\large -\sqrt{16}=-4$$ So when you see something like $$\large \pm\sqrt{16}$$, it is referring to BOTH the positive and the negative square root.

4 years ago
OpenStudy (debbieg):

OK, I'm talking to myself. respond and tag me if you want help understanding.

4 years ago
OpenStudy (tkhunny):

No, you still are missing my point. That silly symbol can mean many things. It depends on what you are doing. So far, you have not stated a specific purpose.

4 years ago
OpenStudy (tkhunny):

Generally, the positive one is the "principal" square root.

4 years ago