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# Plus or minus on roots questions watch

1. Okay so I just wanted to confirm something

So when you have the square root of a number you get plus or minus in your answer

or

But, its not just for square root, whenever the root is a even number you get a plus or minus ... right?

However, if it is to the root of an odd number, you DONT use plus or minus in your answer??

So would this mean that

For n even, give plus or minus?
For n odd, gives positive?

Is this correct? If so, how would this work for when n is negative, or a decimal, or a fraction? What is the general rule? Thanks
Okay so I just wanted to confirm something

So when you have the square root of a number you get plus or minus in your answer

or

But, it not just for square root, whenever the root is a even number you get a plus or minus ... right?

However, if it is to the root of an odd number, you DONT use plus or minus in your answer??

So would this mean that

For n even, give plus or minus?
For n odd, gives positive?

Is this correct? If so, how would this work for when n is negative, or a decimal, or a fraction? What is the general rule? etc
No
3. The reason I've been having trouble with this is that I have been having inconsistency with my answers, for example sometimes the mark scheme has only included the positive answer and sometimes it includes the positive and negative answer and I was wondering if this was the reason. For example

Solve

or

However Solve

or

Mark scheme says its wrong, only including the positive 3
Tthe reason I've been having trouble with this is that I have been having inconsistency with my answers, for example sometimes the mark scheme has only included the positive answer and sometimes it includes the positive and negative answer and I was wondering if this was the reason. For example

Solve

However Solve

Mark scheme says its wrong, only including the positive 3

There are two solutions for this : 1 and -1.

This equation has only one solution : 3. If you cube a negative number you get a negative number so this equation only has a single positive solution.
Okay so I just wanted to confirm something

So when you have the square root of a number you get plus or minus in your answer

or

You are rather confused - there is a sticky in this forum that you should read. But in brief:

says "please write down the +ve number whose square is 9" - so that's +3, since (+3) x (+3) = 9

says "please write down the -ve number whose square is 9" - so that's -3, since (-3) x (-3) = 9

says "please find all of the numbers whose square is 9" - as we have seen, there are two of those, so we write or , or we join those two together and write

However, we *never* write or since the symbol is an order to write down a single, *positive* number.
The reason I've been having trouble with this is that I have been having inconsistency with my answers, for example sometimes the mark scheme has only included the positive answer and sometimes it includes the positive and negative answer and I was wondering if this was the reason. For example

Solve

or

However Solve

or

Mark scheme says its wrong, only including the positive 3
In addition to my previous post:

The equation has two solutions : 1 and -1.

But only.

is incorrect.

Hopefully this doesn't confuse you more
7. (Original post by notnek)

There are two solutions for this : 1 and -1.

This equation has only one solution : 3. If you cube a negative number you get a negative number so this equation only has a single positive solution.
Okay so does this mean that when it is even, (e.g square root, 4th root etc.), there are two solutions, 'plus and minus' and when it is an odd, (e.g cube root, 5th root etc.) then there is one solution, the positive solution?

Okay so does this mean that when it is even, (e.g square root, 4th root etc.), there are two solutions, 'plus and minus' and when it is an odd, (e.g cube root, 5th root etc.) then there is one solution, the positive solution?
http://www.mathopenref.com/rootnumber.html
9. Thank you so much! The website really helped clarify the confusion I was having.

Although the website explained what to do for odd and even degrees, and I assume the same applies for negative degrees. The only other confusion that I can think of left, is how would the rule work for decimal/fractions seeing as they are neither odd or even? Do you just take the positive answer?

For example

or

Thank you so much! The website really helped clarify the confusion I was having.

Although the website explained what to do for odd and even degrees, and I assume the same applies for negative degrees. The only other confusion that I can think of left, is how would the rule work for decimal/fractions seeing as they are neither odd or even? Do you just take the positive answer?

For example

or

Despite what the link says (and I'm glad it gives you some clarity), you must understand that when you write down something to the power of something else or something root something, you're referring to a specific number. It's another thing to find the roof of an equation.

It would depend on the fraction. In the case negative indices, that refers to the variable in the denominator so you'd manipulate the equation till it became the subject.

If you raise the power of the equation to the denominator of a fractional index of a variable then you're left with x to the power of something is = to something else. Whether the number is even or odd will make you aware of how many solutions there are.

11. I see, I'm just so used to hearing stuff like "the square root of a number is plus or minus" that I've gotten confused but instead only applies for say

when solving
it is correct to say

but it would be incorrect to say

from "nowhere" without an equation
I see, I'm just so used to hearing stuff like "the square root of a number is plus or minus" that I've gotten confused but instead only applies for say

when solving
it is correct to say

but it would be incorrect to say

from "nowhere" without an equation
The square root of a number refers to the positive root.

however you are correct in saying that there are two solutions to the equation , namely . This is by convention though. I've heard it said differently.
I see, I'm just so used to hearing stuff like "the square root of a number is plus or minus" that I've gotten confused but instead only applies for say

when solving
it is correct to say

but it would be incorrect to say

from "nowhere" without an equation
Nearly but it should be

always refers to the positive square root only.

It is extremely common for students to be confused by this. I did a mini study on this area a few years back and was amazed by how many teachers and textbooks confuse students with statements like . The old edition of the edexcel C1 textbook contained this exact equation until it was corrected in the later edition.
14. (Original post by notnek)
Nearly but it should be

always refers to the positive square root only.

It is extremely common for students to be confused by this. I did a mini study on this area a few years back and was amazed by how many teachers and textbooks confuse students with statements like . The old edition of the edexcel C1 textbook contained this exact equations until it was corrected in the later edition.
Certainly textbooks differ on whether they say the term square root refers to the positive root of such an equation.
15. (Original post by Kvothe the arcane)
Certainly textbooks differ on whether they say the term square root refers to the positive root of such an equation.
The term "square root" is a bit more wishy-washy than the square root symbol which should always be the positive square root.

You could say that -3 and 3 are both "square roots" of 9. But using the word "the" e.g. "the square root of 9" usually means the positive square root.
The reason I've been having trouble with this is that I have been having inconsistency with my answers, for example sometimes the mark scheme has only included the positive answer and sometimes it includes the positive and negative answer and I was wondering if this was the reason. For example

Solve

or

However Solve

or

Mark scheme says its wrong, only including the positive 3
X^3 is one to one.
Similarly square root function is one to one.
Sqrt(x^2)=|x|={x for x>=0,-x x<0}

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17. (Original post by Kvothe the arcane)
Certainly textbooks differ on whether they say the term square root refers to the positive root of such an equation.
As, notnek said - a number may have 2 square roots but the square root of a number is the positive square root, this is because we define for the map .

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