Q&A for people studying math at any level and professionals in related fields

May 7, 2015 · $\log_2 (3) \approx 1.58496$ as you can easily verify. $ (\log_2 (3))^2 \approx (1.58496)^2 \approx 2.51211$. $2 \log_2 (3) \approx 2 \cdot 1.58496 \approx 3.16992$. $2^ {\log_2 …

Feb 8, 2020 · It is impossible to find the square root of negative one, or the square root of any negative number, because no number times itself can equal a negative number.

Jan 27, 2021 · Legendre's three-square theorem Ask Question Asked 5 years, 2 months ago Modified 1 year, 7 months ago

I just came across this annotation in my school's maths compendium: The compendium is very brief and doesn't explain what this means.

Nov 17, 2013 · That's because the $9$ on the right hand side could have come from squaring a $3$ or from squaring a $-3$. So, when you square both sides of an equation, you can get extraneous …

May 12, 2015 · The square root of i is (1 + i)/sqrt (2). [Try it out my multiplying it by itself.] It has no special notation beyond other complex numbers; in my discipline, at least, it comes up about half as …

If you want the negative square root, that would be $-\sqrt {4} = -2$. Both $-2$ and $2$ are square roots of $4$, but the notation $\sqrt {4}$ corresponds to only the positive square root.

Hence I'm interested in answers suitable for a person that, say, knows what the square root of a square number is, but doesn't know about sequences, functions, convergence and the like.

Jan 2, 2022 · we can square both side like this: $ x^2= 2$ But I don't understand why that it's okay to square both sides. What I learned is that adding, subtracting, multiplying, or dividing both sides by the …