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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,671

Sometimes you might call t =0 today for instance. You could run the equation back to t=-3. That would be 3 days ago. The variable can take negative values.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 510

Is a member trying to indicate that a number in a principal square root must have only one answer?

For instance, if 9 is in a principal square root, must it have only one answer 3?

If I am getting him wrong please correct.

Thanks.

How do you do Bobbym?

I know only one thing - that is that I know nothing

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 510

The fellow's post is at #38.

What is the subtle difference between, a square root and a principal square root?

Thanks.

I know only one thing - that is that I know nothing

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,671

Hi;

The unique nonnegative square root of a nonnegative real number. For example, the principal square root of 9 is 3, although both -3 and 3 are square roots of 9.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 510

So if I am grasping it now, the principal square of a number produces only positive number.

Therefore, the principal square root always infers a positive number.

Am I right?

Please confirm.

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 510

Hi,

Please produce both the principal and the square root signs. So I will know thew properly

I know only one thing - that is that I know nothing

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,671

Therefore, the principal square root always infers a positive number.

I would say yes.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 510

Hi,

I have browsed the link you provided, but couldn't distinguish the principal square root sign from the square root sign.

Some help.

I know only one thing - that is that I know nothing

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

The square root sign

is usually used to indicate the principle square root of a number.Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,671

Hi;

Yep, that means positive root only.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 510

Okay, what name do we give to a negative square root of a number? Since the positive root number has a name.

Thanks in advance.

I know only one thing - that is that I know nothing

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,671

They are called complex or imaginary numbers.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 510

Okay, finally finally.

If I am getting

the whole thing, The square root of 9 is 3 and -3.

the 3 is the prıncipal square root whereas the negative square root -3 is complex or imaginary square root, am I correct?

Please confirm.

I know only one thing - that is that I know nothing

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,671

Both 3 and -3 when squared are 9. But only 3 is the principal square root.

√(-3) is complex or imaginary.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 510

Please do you have an idea as to why it is called complex or imaginary?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,671

It was called imaginary because in the beginning when the concept of the root of a negative number was proposed most mathematicians did not like it. They called them imaginary numbers to sort of poke fun at the whole idea. Later, as it caught on, complex numbers was name given for them.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**EbenezerSon****Member**- Registered: 2013-07-04
- Posts: 510

Thanks for that!

But when 9 is in a square root sign it gives two answers i.e -3 and 3.

if the positive number is the principal square root what name is also given to the -3?

I know only one thing - that is that I know nothing

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,671

When 9 is in the square root sign that means principal square root, just the 3.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

He is asking this:"If we call 3 the principal square root of 9, then what kind of square root of 9 is -3?". The answer is that there is no name given to it.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,671

We could say it is the root of the equation x^2 - 9 = 0.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

We could, but, there is still no special name for non-principal roots.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,671

Everything you are saying is true but you are missing the point of my post #93 which essentially makes your post #94 non - essential.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

Actually, #94 is me feeling you have not understood the question.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,671

Nope, I was dealing with a far more important concept and did not answer that question. Do you see it now?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

But, what you said in #93 was already told and did not need repeating.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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