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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### Should there be an absolute value inside a radical after simplifying the radicals power?

I am trying to help my sibling with math but their teacher seems to want an absolute value inside the radical when simplifying the radical's power, not just outside, which some teachers care and some ...
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### Notation for nth root... can n be non-integer? [duplicate]

We write the nth root of $x$ as $\sqrt[n]{x}$. Can $n$ be non-positive integer? Does the notation $\sqrt[\sqrt{2}]{2}$ or $\sqrt[-3]{8}$ make sense?
551 views

### Correlation between $\sqrt{1/10}$ and length of powers of integers.

I'm searching information about this simple problem involving square roots and length of powers. It's very simple but it seems interesting, at least for me. I'm not a mathematician. Description By ...
1 vote
106 views

### Proving that $\sqrt{x^2+1}+x>0$ for all $x$

Recently while dealing with inverse hyperbolic functions, I came across the expression $$\sinh^{-1}x=\ln(x+\sqrt{x^2+1})$$ We know that $f(x)=\sinh^{-1}x$ is defined for all real values of $x$ since ...
57 views

### Rationalizing higher index roots than cubic, such as $\frac{1}{\sqrt{2}-1}$

so..., someone in here asked about how to rationalize higher index roots, they sad something about the telescoping identity, but I don't get it. I know there is another way to do it and has something ...
56 views

### How to find derivative in radical function?

I need to find derivatives of following functions: $$\frac32x^\frac32-\frac{2x^2}{3}$$ $$-2\sqrt{x}-\frac{-2}{\sqrt{x}}$$ So starting from first one, I have tried to first simplify the fractions to ...
80 views

I'm having some trouble with this problem: a, b, c are positive real numbers where $\sqrt a + \sqrt b + \sqrt c = 1$ . Prove the following inequality: $$\frac{a^2 + bc}{\sqrt{2a^2(b+c)}} + \frac{b^2 ... 5 votes 2 answers 146 views ### Why isn't \sqrt{64x^4y^8z^6} equal to 8x^2y^4z^3? I simplified$$\sqrt{64x^4y^8z^6}$$by taking the square root of 64 (getting 8), x^4 (getting x^2), y^8 (getting y^4), and z^6 (getting z^3). My answer, 8x^2y^4z^3, not quite right ... 2 votes 2 answers 66 views ### Determine if a number n is a power What would be an efficient algorithm to determine if n \in \mathbb{N} can be written as n = a^b for some a,b \in \mathbb{N}, b>1? So far, I've tried: ... 0 votes 0 answers 42 views ### When does squaring the square root of a function give me the absolute value of the function Why does [\sqrt{f(x)}]^2=f(x)  , but \sqrt{g^2(x)}=|g(x)| ? -1 votes 1 answer 64 views ### Find closest integer to (3+\sqrt7)^4 by hand [duplicate] Find the closest integer to$$(3+\sqrt7)^4$$by hand, without knowing the correct value of \sqrt7 (Maybe just knowing that 2<\sqrt7<3). My work:$$(3+\sqrt7)^4 = (16+6\sqrt7)^2 = 508+192\...
I'm following a tutorial which says this: Convert the following equation to a pair of parametric equations for $x$ and $y$ in terms of $t$: $$y=x^2+3$$ Step 1 - Set $t$ equal to $x^2$: $$t=x^2$$ Step ...