calculus - Getting rid of square root in this integration
Getting rid of square root in this integration. Ask Question Asked 10 years, 6 months ago.
Square root inside a square root - Mathematics Stack Exchange
Jun 24, 2014 · The square root of the square root of x is therefore $$\sqrt{\sqrt x} = (\sqrt x)^{1/2} = (x^{1/2})^{1/2} = x^{1/4} = \sqrt[\large 4] x$$ Since the domain of $\sqrt x$ is $[0, + \infty)$ , this is also the domain of $\sqrt{\sqrt x} = x^{1/4}$ .
Getting rid of the square roots in the expression
In general, the polynomial relation will have $2^n$ distinct 'roots' for the one non-square-root variable of the original expression in terms of the other variables. $\endgroup$ – Steven Stadnicki Commented Nov 14, 2013 at 17:52
Whats the rule for putting up a plus-minus sign when taking …
Using the x^2=49 example, there is no logical need for the symbol on the right when we take the square root, because the square root of 49 is 7, by definition. But when we take the square root of the left hand side, we must also arrive at a positive number (by definition).
Eliminating square roots in trig identities (Integrating square roots)
If $1 + \cos 2\theta = 2 \cos^2 \theta$, then $$1 - \cos 2\theta = 2 \sin^2 \theta,$$ because by adding these two equations together, you would get $$2 = 2 \cos^2 \theta + 2 \sin^2 \theta,$$ where upon dividing by $2$ you recover the circular identity $$1 = \cos^2 \theta + \sin^2 \theta.$$ Consequently, $$\frac{1 - \cos 2\theta}{2} = \sin^2 \theta,$$ and taking square roots gives …
Why eliminate radicals in the denominator? [rationalizing the ...
The usual reason I've heard is that dividing by integers is computationally easier -- it's easier to find, say, $(5\sqrt{3})/3$ by computing $5 \times \sqrt{3} \approx 8.66 $ and then dividing by $3$ to get $2.89$ then to find $5/\sqrt{3}$ by dividing $5/1.73$ directly.
How to remove roots from an equation? - Mathematics Stack …
Feb 26, 2021 · How to extract square roots of polynomials in several variables? 6 Finding a monic polynomial with integer coefficients having $\sqrt{2} + \sqrt{3} + \sqrt{5} + \sqrt{7}$ as one of its roots.
Is there a way to get rid of all square roots in an equation with
Nov 3, 2016 · There are a few possibilities at the start with how many terms you'll have at either side of the equals sign before you square: constant = 4 roots --> results in constant = 6 roots. constant+root = 3 roots --> results in constant + root = 3 roots. constant+ 2 roots = 2 roots --> results in constant + 3 roots = root
calculus - finding the derivative of a square root function ...
Getting rid of square root in this integration. 0. finding the derivative of a square root function .. 1.
Solving limits with square roots - Mathematics Stack Exchange
Jul 8, 2015 · Taking limits with a square root in a quotient. 1. Solving given limit with other limits. 1.