Math Is Fun Forum

Anakin

Member

Registered: 2009-10-04

Posts: 145

The Square Root

Alright so I was bored and always wondered this. I was looking at the Site Suggestions forum (I think) and I came across a thread named "What is a Function?" and something about square roots was mentioned.

So my question is, just for general knowledge:

For the first one, the answer is ONLY positive two, I believe. That is because we are asking for the positive square of 4. Correct?
But for the second one, the horizontal asymptotes are at y=2 and y=-2. Why is it that with the second one we have to consider the denominator as  +/-

?

Thanks for having a look. I was just curious.

Vercingetorix

Member

Registered: 2009-11-03

Posts: 21

Re: The Square Root

Hi Anakin,

This is because the square of a negative or positive always results in a positive.

It may help to think of it as:

Last edited by Vercingetorix (2009-11-05 11:13:34)

Anakin

Member

Registered: 2009-10-04

Posts: 145

Re: The Square Root

That's what I figured and when I asked my pre-calculus teacher, he said it's only positive two because it's not a function or something like that.

http://www.mathisfunforum.com/viewtopic.php?id=7528
And according to this thread, the posters agree that it is only a positive number unless the square root has a

in front of it.

Any idea?

Last edited by Anakin (2009-11-05 11:18:22)

Vercingetorix

Member

Registered: 2009-11-03

Posts: 21

Re: The Square Root

I stand corrected.  Your teacher is correct, because with a constant like 4 you already know the sign.  When there is a function with an unknown (such as x), it may be positive or negative and hence the ± sign.  Sorry for the bum steer to begin with.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: The Square Root

The denominator is always positive (when it exists), but the numerator can sometimes go negative. That's why the function can take a negative value.

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Why did the vector cross the road?
It wanted to be normal.

Anakin

Member

Registered: 2009-10-04

Posts: 145

Re: The Square Root

So therefore, when you're taking the square root of a variable, it can be positive or negative?

But if it's a constant, it's only positive, right?

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: The Square Root

The radical sign means the principal (ie positive) square root:

However, "square root" is the value "x" in:

which can be positive or negative:

and

Hopefully explained on my new page:  Squares and Square Roots in Algebra

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Sarah12

Guest

Re: The Square Root

Anakin that is Geometry.

Anakin

Member

Registered: 2009-10-04

Posts: 145

Re: The Square Root

Thanks for the clarification MathisFun. Makes more sense now.

Anakin

Member

Registered: 2009-10-04

Posts: 145

Re: The Square Root

One more thing. Does that mean the SQUARE ROOTS of 4 are positive 2 and negative 2? But the principal square roots (symbolized by the use of a radical sign) is only positive 2?