Linked Questions
29 questions linked to/from Is $\sqrt{64}$ considered $8$? or is it $8,-8$?
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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 ...
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3
votes
2
answers
700
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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 ...
6
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5
answers
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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 ...
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4
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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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4
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2
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338
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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.
...
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4
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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 ...
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4
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Square root of 4 equals 2 (or) ±2? [duplicate]
Simple yet much debated question inside my study circle. Please explain with reasons.
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2
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112
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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 ...
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1
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Problem with square roots and squares [duplicate]
Suppose we have
$$ x^{2} = (-x)^{2}.$$
I understand that this equation holds because
$$\begin{aligned}
(-x)^{2} & = (-1\cdot x)^{2} \\
& = (-1)^{2} \cdot x^{2} \\
& = x^{2},
\end{aligned}$$...
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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 ...
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6
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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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38
votes
5
answers
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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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5
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Mistake in solving an equation involving a square root
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 ...
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What happens when square root is performed in inequalities?
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 > ...
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2
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Why $f(x) = \sqrt{x}$ is a function?
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 ...
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