What is the Meaning of Taking Square? - Explained

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Taking the square of a number involves multiplying it by itself, which is a fundamental mathematical operation. In physics, squaring quantities like velocity or time often arises from the derivation of formulas, such as those calculating energy. While some argue that squared terms in physical laws are significant, others contend that there is no inherent physical meaning to squaring a quantity. The discussion highlights that kinetic energy, for example, is a scalar and always positive, but this does not imply a deeper physical interpretation of squaring. Ultimately, the relationship between mathematical operations and their physical implications remains complex and often debated.
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Taking square?

Why do we need to take square? What does it mean? For instance, calculating energy, why do we need to take square of the velocity or taking square of time in some other formulas?

In general, what is the mathematical meaning of taking square?
 
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Naimbora said:
Why do we need to take square? What does it mean? For instance, calculating energy, why do we need to take square of the velocity or taking square of time in some other formulas?

In general, what is the mathematical meaning of taking square?
The mathematical meaning of taking the square (of a number) is simply multiplying a number by itself, raising it to the second power etc. In the case of a vector this means taking the scalar product of the vector with itself.

The physical interpretation on the other hand is something completely different.
 


Hootenanny said:
The physical interpretation on the other hand is something completely different.

Ok, i think that i asked the question in a wrong way.. I did mean the physical interpretation of "taking square" as Hootenanny said above.

Could you help me about this question, at least a personal idea or expression?
 


Naimbora said:
Could you help me about this question, at least a personal idea or expression?
There is nothing particularly special about a squared quantity, the fact the some quantity is squared simply arises as a matter of course from their derivations.

Of course, some people would say that its strange that so many physical laws contain powers of two; but conversely there are many that don't. Personally, I don't feel that there is any special physical interpretation to physical laws or equations containing terms to the second power.

Of course, one can draw conclusions from certainly formulae. For example, you cite kinetic energy; from this equation one can conclude firstly that kinetic energy is a scalar quantity and secondly that kinetic energy is always positive.
 


Thank you, Hootenanny. I seem to get barked at everytime I make the point that mathematical concepts do NOT have "physical meaning".
 
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