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# Positive & Negative Square Roots watch

When finding the square root of a number must one always give both positive and negative roots? Or are there instances where only the positive root is required?

Can you help me make the distinction of what questions require what?

I know that when asked to solve Quadratics there will have to be two answers (except in some cases where a negative number is invalid) since we are solving for X and it could be either the positive or negative square root. But what about something like the square root of 36. Is it just 6 or is it positive, negative 6?

Any help would be greatly appreciated!
2. Most quadratic equation questions require you to give both roots. e.g. as you said x2 - 36 = 0
However you might also come across a question like (ln x)2 - 36 = 0 in which you would have to leave out the negative root
3. (Original post by shawn_o1)
Most quadratic equation questions require you to give both roots. e.g. as you said x2 - 36 = 0
However you might also come across a question like (ln x)2 - 36 = 0 in which you would have to leave out the negative root
That makes sense, thank you.

But what about when only dealing with constants, such as the square root of 64. Would the answer be 8 or plus and minus 8?
4. (Original post by L'Eternité)
That makes sense, thank you.

But what about when only dealing with constants, such as the square root of 64. Would the answer be 8 or plus and minus 8?
Depends on the context of the question, if it's just to solve the equation then give both roots, if it's to solve a real life problem (like in mechanics) then give only the positive root
5. (Original post by L'Eternité)
That makes sense, thank you.

But what about when only dealing with constants, such as the square root of 64. Would the answer be 8 or plus and minus 8?
It depends on how the question is written.

Technically, a positive constant has two square roots. e.g. √a and -√a

64 has two square roots, -8 and 8 but when the radical sign is used (√) then it refers only to the principal square root (i.e. the positive square root)

√64 = 8, not -8 where as -√64 = -8
6. (Original post by L'Eternité)

When finding the square root of a number must one always give both positive and negative roots? Or are there instances where only the positive root is required?

Can you help me make the distinction of what questions require what?

I know that when asked to solve Quadratics there will have to be two answers (except in some cases where a negative number is invalid) since we are solving for X and it could be either the positive or negative square root. But what about something like the square root of 36. Is it just 6 or is it positive, negative 6?

Any help would be greatly appreciated!
http://www.thestudentroom.co.uk/show....php?t=3173187
7. that really is a heroic post

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