Yes or no, Can you square root a zero

In summary, the conversation discusses the concept of taking the square root of zero and how it relates to limits. It is established that the square root of zero is indeed zero, but when dealing with limits, the question of approaching zero from the left or right must be considered. Furthermore, the conversation touches on the idea of imaginary numbers and how they are not applicable in certain situations. Lastly, the conversation briefly mentions the Doppler Shift formula and how it involves the square root of a quotient, which may pose a problem if the denominator is equal to zero.
  • #1
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Yes or no, Can you square root a zero. This is for a limits question.
 
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  • #2
yes and the answer you get is 0 and u don't have to worry about +/- obviously

The square root of 0 is 0. In mathematics, when you multiply 0 by itself (0 * 0), the result is 0, so the square root of 0 is indeed 0.

Yes, you can take the square root of zero. The square root of zero is still zero. In mathematical notation:

√0 = 0

This is because when you multiply zero by itself (0 * 0), you get zero. So, the square root of zero is indeed zero.
 
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  • #3
Does anyone have any good sites that can help me with limits
 
  • #4
If youre asking about the limit of [tex]\sqrt{x}[/tex], you can only approach it from the right. Because the limit point is unapproachable from the left, the limit does not exist. Remember, its not a polynomial so you can't just plug it in
 
  • #5
Ahh it is approachable from the left, but is imaginary. So the limit from the left exists, but isn't the same as the limit from the right, so the general limit does not exist.
 
  • #6
[tex]\sqrt{x}[/tex] is DEFINED to be the POSITIVE square root. In this sense it is undefined for x<0 (neither square root is 'positive').To consider the limit from the left you would have to make a choice of definition of square root that would select one of the square roots for x<0 as well. No matter which way you do this you would still get 0 as the left hand limit.
 
  • #7
If you make the rather basic assumption that the question was posed over reals in an R^2 Cartesian plane, than imaginary numbers are not up for discussion. Furthermore, the concept of order (less than, greater than) dissolves in the complex number system, which makes delta-epsilon pretty hard to do
 
  • #8
Order may go, but you still have the notion of |x|<epsilon. You can still discuss limits and continuity perfectly well.
 
  • #9
I am also eager for an answer to this question though it is for different reasons. Due to a poor choice in essay questions :) , I am trying to calculate the Doppler Shift in light if one were to be traveling in a car at the speed of light and turn on their headlights. This, I think, should be calculated with the Relativistic Doppler Shift Formula. In the end this leaves me with the square root of a quotient, of which, the denominator is velocity over c plus negative one, or zero. This is not the final quantity of the solution but rather one quantity involved. Does this leave me with an answer that is undefined( making it not possible to have an answer?) or do I have the square root of zero equaling zero therefore simply plugging zero into the equation? PLEASE HELP :) thanks
 
  • #10
The square root of zero is zero. No doubt about that. If you get a formula with zero in the denominator you have a problem. That's not defined. The v is the doppler shift formula is a relative v between a source and an observer. Who's the observer? In a physical situation it's not possible for v to reach c. You can only ask what happens as v approaches c.
 
  • #11
So I do not hijack this thread I think I should post my full inquiry on a fresh thread.
 
  • #12
Good idea. You'll get more notice that way as well.
 

1. Can you really square root a zero?

Yes, you can square root a zero. The square root of zero is zero itself.

2. Is the square root of zero a real number?

Yes, the square root of zero is a real number. It is the only number that when multiplied by itself, gives zero as the result.

3. What is the difference between the square root of zero and zero to the power of two?

The square root of zero is a single number, zero. However, zero to the power of two is an expression that can mean any number multiplied by itself two times, which can result in zero or non-zero values.

4. Can you show me the mathematical proof that the square root of zero is zero?

The mathematical proof is as follows: if a number x squared equals zero, then x must also equal zero. This is because the only number that when multiplied by itself gives zero as the result is zero itself.

5. Is the concept of square root of zero useful in any real-life applications?

The concept of square root of zero may not have direct applications in real-life situations. However, it is a fundamental concept in mathematics and is used in various mathematical and scientific calculations and equations.

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