What exactly is the purpose of square-rooting

[Niaboc67]

I am sure there must be some ultimate purpose to it. But I just don't understand what the point is of square-rooting. All the math I do is abstract and doesn't apply to real-world situations and the physical world. Is there something to square-rooting numbers that is relatable to the real-world?

Please explain
Thank you

 

[Fredrik]

The super obvious example is that if the area of a square is $A$, then the edge length is $\sqrt{A}$. But there are of course lots of other examples where square roots are useful. My favorite example is from special relativity, which says that if two clocks are at the same location, but one of them is moving with speed v relative to the other, then an observer comoving with one of the clocks will conclude that the ticking rate of the other clock is slow by a factor of
$$\frac{1}{\sqrt{1-\frac{v^2}{c^2}}},$$ where c is the speed of light in a vacuum, 299792458 m/s.

Are these the sort of examples that you want to see?

 

[mfb]

If you go 3 meters to the north and 3 meters to the east, then you are $\sqrt{3^2+4^2}=5$ meters away from your original location.

An object falling down by d=5 meters will need $\sqrt{\frac{2d}{g}} \approx 1s$ to reach the ground (where $g=9.81\frac{m}{s^2}$).

...

 

[Mark44]

A carpenter friend of mine asked me a question about installing a ceiling light fixture. The part of the fixture that was fastened to the ceiling was circular, with a diameter of 6". He wanted to know how large a square hole he could cut in the ceiling so that the square opening was hidden by the fixture. Using simple trig gives an answer of $\sqrt{18} = 3\sqrt{2} \approx 4.2 \text{ inches}$.

 

[zoki85]

" Let no man ignorant of geometry enter here " - Plato

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[HallsofIvy]

I am sure there must be some ultimate purpose to it. But I just don't understand what the point is of square-rooting. All the math I do is abstract and doesn't apply to real-world situations and the physical world. Is there something to square-rooting numbers that is relatable to the real-world?

Please explain
Thank you

If your "real- world" consists of saying "would you like fries with that", there is absolutely no use for square roots!