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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.
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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)
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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
Any idea?
Last edited by Anakin (2009-11-05 11:18:22)
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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.
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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.
Why did the vector cross the road?
It wanted to be normal.
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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?
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The radical sign means the principal (ie positive) square root:
However, "square root" is the value "x" in:
which can be positive or negative:
andHopefully explained on my new page: Squares and Square Roots in Algebra
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
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Anakin that is Geometry.
Thanks for the clarification MathisFun. Makes more sense now.
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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?
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