If you square root something, then you have to put a ±. Do you do the same for cube roots?

[xxscienceboyxx]

If you square root something, then you have to put a ±. Do you do the same for cube roots?
Like for example sqrt(4) would be ±2. But for something like cube root of 27 would the answer be ±3 or just +3?

 

[tkhunny]

1) "square root" isn't a verb.
2a) [math]\sqrt{4} = 2[/math] - No + or - about it.
2b) The solutions to [math]x^{2} = 4[/math] are x = 2 or x = -2.
It maters what you are doing, not so much the symbols you encounter.

 

[Dr.Peterson]

If you square root something, then you have to put a ±. Do you do the same for cube roots?
Like for example sqrt(4) would be ±2. But for something like cube root of 27 would the answer be ±3 or just +3?

Assuming you are talking about what you do when solving an equation involving a cube, so that you take the square root (tkhunny's 2b):

Think about why you use the ± when you do that.

Then think about whether that reason applies when you take a cube root.

Or, if you'd rather have something concrete to think about, take any such equation you've been given, and then see whether the solution will be correct if you use ±.

Then show us your conclusions.

 

[Steven G]

Check for yourself, it is not that hard.

The cubert(27) = 3. Is this correct? Lets see. Is 3^3 = 27? Yes it is, so cube root of 27 = 3.
The cubert(27) = -3. Is this correct? Lets see. Is (-3)^3 = 27. No!, so cube root of 27 is not -3.

 

[xxscienceboyxx]

Check for yourself, it is not that hard.

The cubert(27) = 3. Is this correct? Lets see. Is 3^3 = 27? Yes it is, so cube root of 27 = 3.
The cubert(27) = -3. Is this correct? Lets see. Is (-3)^3 = 27. No!, so cube root of 27 is not -3.

Ohh. That makes sense. Thanks! I get it now. For something like a square root on the otherhand, sqrt(4) can be -2, because (-2)^2 can be 4.

 

[Steven G]

Ohh. That makes sense. Thanks! I get it now. For something like a square root on the otherhand, sqrt(4) can be -2, because (-2)^2 can be 4.

While I agree that (-2)^2 = 4 I can not agree that sqrt(4) = -2. Have you ever seen the sqrt graph?? Mathematicians wanted y = sqrt(x) to be a function. Remember to be a function it can't be that you plug in x=4 and get back that y = 2 or y=-2. You can't get back two values for one input. So to make y = sqrt(x) a function we do not allow any negative answers. That is why sqrt(4) is NOT -2.

Also please do not say that (-2)^2 can be 4. Instead say that (-2)^2 IS 4.

Note that if you were solving the equation x^2 = 4, then x can be + or - 2. However x = sqrt(4) has one answer and that is x=2.

 

[JeffM]

I fear you may have misheard your teacher on a very subtle point, or your teacher may not have wanted to get into this complexity.

In the real number system, each real number > 0 has two square roots, one positive, one negative. Zero has one square root, namely itself, and negative real numbers have no real square root at all.

But the square root FUNCTION is defined as non-negative.

[MATH]x \ge 0 \implies \sqrt{x} \ge 0 \text { and } - \sqrt{x} \le 0.[/MATH]
There are two square roots of a positive real number, the non-negative one indicated by the square root symbol, the non-positive one indicated by a minus sign before the square root symbol. The same goes for every even root of a positive real number.

In the real number system, every number has one cube root. If the number is positive, so is the cube root. If the number is negative, so is the cube root. If the number is zero, the cube root is zero. And the cube root function does need to be not defined in terms of sign because each is unique. The same goes for every odd root of a real number.

With respect to even roots, we need a way to distinguish between the positive and negative ones. We do that by saying the root symbol refers to the positive one.

Got it? It is a tricky little point.

 

[Otis]

… for example sqrt(4) would be ±2 …

Hi scienceboy. I don't know whether or not you've been introduced to the concept of 'function' in math, but do you have a textbook?

If so, look up "principle square root".

Please tell me also whether you've learned about 'absolute value', yet. Thanks!

?

 

[Saumyojit]

I fear you may have misheard your teacher on a very subtle point, or your teacher may not have wanted to get into this complexity.

In the real number system, each real number > 0 has two square roots, one positive, one negative. Zero has one square root, namely itself, and negative real numbers have no real square root at all.

But the square root FUNCTION is defined as non-negative.

[MATH]x \ge 0 \implies \sqrt{x} \ge 0 \text { and } - \sqrt{x} \le 0.[/MATH]
There are two square roots of a positive real number, the non-negative one indicated by the square root symbol, the non-positive one indicated by a minus sign before the square root symbol. The same goes for every even root of a positive real number.

In the real number system, every number has one cube root. If the number is positive, so is the cube root. If the number is negative, so is the cube root. If the number is zero, the cube root is zero. And the cube root function does need to be not defined in terms of sign because each is unique. The same goes for every odd root of a real number.

With respect to even roots, we need a way to distinguish between the positive and negative ones. We do that by saying the root symbol refers to the positive one.

Got it? It is a tricky little point.

is this something to do with my post

 

[JeffM]

is this something to do with my post

Not at all. I was responding to the poster. I would never post a response to A in a thread of B’s.

 

[Saumyojit]

Not at all. I was responding to the poster. I would never post a response to A in a thread of B’s.

I found some relevance but that post is still unclear to me . Too many confusions i dont know what are the major takeaways i should take from that post

 

[JeffM]

I found some relevance but that post is still unclear to me . Too many confusions i dont know what are the major takeaways i should take from that post

Which post? Some post I made in one of your threads? Some post I made in this thread? If the latter, I was trying to address what seemed to me to be behind the questions of this poster, not some unknown question of yours. Let’s not take over someone else’s thread with your unspecified questions about some unspecified post.

 

[Saumyojit]

Which post? Some post I made in one of your threads? Some post I made in this thread? If the latter, I was trying to address what seemed to me to be behind the questions of this poster, not some unknown question of yours. Let’s not take over someone else’s thread with your unspecified questions about some unspecified post.

Complex no post .

 

[JeffM]

Complex no post .

If you have a question about some post in YOUR complex number thread, ask it there and give a post number. As it is you are interfering with another student’s thread. STOP IT OR I SHALL ASK TO HAVE YOU BANNED.

 

[Saumyojit]

If you have a question about some post in YOUR complex number thread, ask it there and give a post number. As it is you are interfering with another student’s thread. STOP IT OR I SHALL ASK TO HAVE YOU BANNED.

OK it was my mistake . sorry