Linked Questions

I got to thinking about the square root the other day, and there's this thing that bugs me in the back of my mind. As far as I know, $\sqrt{4}$ is unambiguously $2$, and nothing else, as the square ...

I recently saw someone say: $\sqrt{x}$ is, by definition, positive Which didn't sit easily with me as we always say $\pm$ for any square root. Then it got me thinking that if, by definition, the ...

I solved the equation $\sqrt{6-5x}=x$ as follows: $$(\sqrt{6-5x})^2=x^2$$ $$6-5x=x^2$$ $$0=x^2+5x-6=(x+6)(x-1)$$ $$x=-6 \quad \text{or} \quad x=1$$ If I plug in $x=-6$ into the original equation, I ...

I have being told all my life that $\sqrt{9}$ equals to $\pm3$. That all changed when I saw a video talks about it. It said that the square root does not spit out a negative number. I wanted to see if ...

While practicing math for the SAT, I came across the question- What is the sum of the solutions to $\sqrt{3x+13} = x+3$? The first step I did was to make it a quadratic from the given equation. ...

If you were to ask me what the square root of 25 is, I would quickly say 5. But is that the correct answer? Or is the true answer actually 5 OR -5? In other words, does the square root of a real, ...

Simple yet much debated question inside my study circle. Please explain with reasons.

It's basic question, but sometimes might confuse me. Why do we adding the plus minus sign $(\pm)$ after take a root of something? And why sometimes we just write the plus term only. I can't give a ...

Suppose we have $$ x^{2} = (-x)^{2}.$$ I understand that this equation holds because $$\begin{aligned} (-x)^{2} & = (-1\cdot x)^{2} \\ & = (-1)^{2} \cdot x^{2} \\ & = x^{2}, \end{aligned}$$...

Can the square root of a real number be negative? Dealing with the questions of functions in eleventh class my maths teacher says that square root of a real number is always positive. How is it ...

It is perhaps a bit embarrassing that while doing higher-level math, I have forgot some more fundamental concepts. I would like to ask whether the square root of a number includes both the positive ...

I want to solve $2x = \sqrt{x+3}$, which I have tried as below: $$\begin{equation} 4x^2 - x -3 = 0 \\ x^2 - \frac14 x - \frac34 = 0 \\ x^2 - \frac14x = \frac34 \\ \left(x - \frac12 \right)^2 = 1 \\ x ...

Simplify: $x^2 > 1$. My solution: Taking square root on both sides: $±x > ±1$ So my results are: $x > 1$ $x > -1$ $-x > 1$ $\implies$ $(-1 > x)$ $-x > -1$ $\implies$ $(1 > ...

Why $f(x) = \sqrt{x}$ is a function (as I found in my textbook) since for example the square root of $25$ has two different outputs ($-5,5$) and a function is defined as "A function from A to B is a ...

What is the domain and range of real function $f(x) = \sqrt{9 − x^2}$? In order to find the function's domain, you need to take into account the fact that, for real numbers, you can only take the ...