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May 12, 2015 · Since it's continuous, the square root of any positive real number is always a well-defined positive real number: Given the positive gap-between-rationals which you want to take the square root of, the square root is the positive gap-between-rationals such that any rational greater than the square-root-gap squares to a rational greater than the ...

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.

The suaqre root of a (non-negative) real number is non-negative by definition, but is there a similar decision for "the" square root of other (complex) numbers? $\endgroup$ – Wolfgang Kais Commented Jul 8, 2023 at 17:59

$\begingroup$ Minor point: I notice quite a few elementary algebra books as well as some writers here taking the view that the n-th root of x is defined as x to the power 1/n. I disagree strongly. I disagree strongly.

Jun 24, 2014 · The square root of the square root of x is therefore $$\sqrt{\sqrt x} = (\sqrt x)^{1/2} = (x^{1/2})^{1/2} ...

As traditional known the square root of any number would have two result, its cube root would have three ...

Jan 16, 2015 · The reason that often only the Taylor series for $\sqrt{1 + x}$ is given in the books is that – for the square-root function – the general case can easily be reduced to the special case: $$ \sqrt {\mathstrut x} = \sqrt {\mathstrut x_0 + x - x_0} = \sqrt {\mathstrut x_0}\sqrt {1 + \frac {\mathstrut x-x_0}{x_0}} $$ and now you can use the ...

May 18, 2018 · The square root of 289 is 17 So let put 289 in the house. sqrt(289) So the doorbell is literally a 2 unless it states otherwise. So this is asking us what number times itself gives us 289. So when we plug sqrt(289) into our calculator, we get 17. But do we know if it correct? Let square 17. 17^2 = 289 So we know this work or we could of #17*17=289. Either way of …

I have a question regarding taking square roots in inequalities. I have a problem asking: Suppose $3x^2+bx+7>0$ for every real number x. Show that $|b|<2\\sqrt{21}$. In an earlier question i...

In fact you can take any two numbers which can be added to get 2 (not nesserly 0.01 but at least you should know the root of one of them So for example $\sqrt{2} = {(1+1)^{1/2}}$ Know all what you need is to expand it using bio theorem and for 2 terms you ll get 1.5