# Questions tagged [radicals]

For questions involving radical of numbers or radical of expressions (i.e. numbers/expressions raised to the power of a fraction).

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### For $x\geq 0$, is $\sqrt{x}$ the magnitude of $x^{1/2}$?

Motivation \begin{align} 4^{1/2} &= \begin{cases} \left(2^2\right)^{1/2}\\ \left(\left(-2\right)^2\right)^{1/2} \end{cases} \\ &= \begin{cases} 2\\ ...
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1answer
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### Dungeons & Dragons 3.5 Experience

I built a spreadsheet that accurately determines a character's level by looking at the experience. You can find a chart of this here: https://www.ign.com/wikis/dungeons-and-dragons/...
6answers
107 views

### Is $x=-2$ a solution of the equation $\sqrt{2-x}=x$?

Solve the equation: $$\sqrt{2-x}=x$$ Squaring we get $$x^2+x-2=0$$ So $x=1$ and $x=-2$ But when $x=-2$ we get $$\sqrt{4}=-2$$ But according to algebra $$\sqrt{x^2}=|x|$$ So is $x=-2$ invalid?...
4answers
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### What is the square root of $(-5)\cdot(-5)$ and how is it different from $\sqrt{(-5)^2}$?

What is the square root of $(-5)\cdot(-5)$ and how is it different from $\sqrt{(-5)^2}$? Can anybody explain?
2answers
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### Compute the integral $\int\limits_0^1 \frac{3x}{\sqrt{4-3x^2}} dx$?

I am struggling to compute the following equation. \begin{equation} \displaystyle\int_0^1 \dfrac{3x}{\sqrt{4-3x^2}} dx \end{equation} We are expected to use u-substitution, but I'm stuck and ...
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### Equivalency of two radical expressions proof

I know that $$\sqrt{2+2\sqrt{2}}-\sqrt{1+\sqrt{2}}$$ is equivalent to $$\sqrt{\sqrt{2}-1}.$$ However, I do not know how to prove that one is equal to the other and vice versa. The cause that I want to ...
1answer
262 views

### $S=\sqrt{1}+\sqrt{2}+\sqrt{3}+\sqrt{4}+\dots+\sqrt{m}$ is almost an integer. Find $m$

For an integers $m$ and $n$, $1<m\le n$ , we need to find the best $m$ so that $S=\sqrt{1}+\sqrt{2}+\sqrt{3}+\sqrt{4}+\dots+\sqrt{m}$ is almost an integer. Example: when $n=40$, then the best ...
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### Constraints of $\frac{\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}}{\sqrt{x}+\sqrt{y}}$

We have the expression A= $\frac{\sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}}{\sqrt{x}+\sqrt{y}}$. I have to simplify it. First I want to define the constraints of $x$ and $y$ but I have some ...
4answers
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