May 19, 2019 · $\begingroup$ 6*6=36, and this forms a square of side 6. But 9*4=36, but this forms a rectangle of sides, 9 and 4. So we see that 36 can be interpreted as a square as well as a rectangle. Where as, 1,4,9,25, etc. has just one representation of a square of side, 1,2,3,5 respectively. $\endgroup$ –

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The general guideline of writing the square root as a fractional power and then using the power and chain rule appropriately should be fine however. Also, remember that you can simply pull out a constant when dealing with derivatives - see below.

Apr 21, 2017 · Most instructors prefer these as well. @GEdgar provides useful insight there on a possible distinction. Though I always prefer to restate my conclusion anyway, coming full circle - in my view it truly finishes off a proof. I only ever see the empty square $\square$ on stackexchange where I have presumed people were lazy with their LaTeX.

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It is because the square is somehow "applied" on the function. For function, you will probably often encounter this notation, and that is because, it is the function itself that is squared, not just the value.

The standard deviation, however (the square root of the variance) is again measured in seconds, so it measures something similar (at least, physically similar). As for why we like the square-root-of-average-of-squares better than the average-of-absolute-values - the square has better mathematical properties, as shown in other answers and in the ...

When you first square 31, you get 961...which you can immediately reduce mod 773 to get 188. You square that...and reduce mod 773 again. You square that...and reduce mod 773 again. And you find that you're never sqauring a number larger …

Mar 14, 2016 · The irrationality of the square root of 2 follows from our knowledge of how Pythagorean triples behave, specifically, that for positive integers x, y, and z, if x^2 + y^2 = z^2, then x is not equal to y. But if the square root of 2 were rational, then there would exist positive integers a and b such that a/b = the square root of 2. Then a^2/b^2 ...

Taking the square of a finite series. 2. Knuth summation clarification. 21. Unambiguous summation notation. 7.