1 vote
258 views

### Soft question about the square root [duplicate]

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 ...
• 2,434
2k views

### is $\sqrt{x}$ always positive? [duplicate]

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 ...
3k views

### Is it more correct to say that the square root of 25 is equal to 5 OR -5? [duplicate]

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, ...
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1k views

### Square root of 4 equals 2 (or) ±2? [duplicate]

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

### Why does the definition of a square root for a number not include its solution's negative counterpart? [duplicate]

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. ...
• 43
337 views

### Why is the solution to $\sqrt{6-5x}=x$ only $x=1$ and not $x=-6$? [duplicate]

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 ...
• 61
188 views

### Does the square root spit out a negative result? [duplicate]

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 ...
1 vote
199 views

### What is the value of $\sqrt{(-4)^2}$? (Sorry for the triviality!) [duplicate]

I started a debate in a youtube video (something you should never do...) because of this question. For me, the answer has to be $-4$, simplifying powers for example. But I don't know if I'm having ...
302 views

### The plus minus sign after take a root of terms [duplicate]

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 ...
• 2,220
71 views

### Problem with square roots and squares [duplicate]

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}...
28 views

### Range of Square Root of X [duplicate]

The $f(x)=\sqrt{x}$ has a domain of $[0,\infty)$. As of in our textbook it is written that range is also $[0,\infty)$. How? $\sqrt{x}=-\sqrt x\space or \space \sqrt x.$ According to me range should be ...
• 163
113k views

### Can the square root of a real number be negative? [duplicate]

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 ...
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11k views

### Square roots -- positive and negative

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 ...
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2k views

### Mistake in solving an equation involving a square root

I want to solve $2x = \sqrt{x+3}$, which I have tried as below:  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 > ...