Square root of x squared?

Clydey

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I've decided to do something of a math refresher course, and it seems to be going well. However, I ran into a notation I didn't recognise, and I couldn't find it used elsewhere (I tried copy and pasting it into google). It seems to mean the square root of x squared, as far as I can tell. Can anyone confirm or supply an explanation? Here's the relevant image:

xsquared.jpg

Until I saw that image, I would have assumed that notation meant 2^x. Can anyone explain what I'm missing? It would be greatly appreciated.
 

MarkFL

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Hello, and welcome to FMH! :)

What that means is \(x\) times \(\displaystyle \sqrt{2}\). Personally, I would choose to write this as:

\(\displaystyle \sqrt{2}x\)
 

Clydey

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Hello, and welcome to FMH! :)

What that means is \(x\) times \(\displaystyle \sqrt{2}\). Personally, I would choose to write this as:

\(\displaystyle \sqrt{2}x\)
Thanks for the response. That makes more sense. I should have thought of that. Presumably the index would be inside the v portion of the radical symbol?
 

MarkFL

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Converting from radical to exponential form, we use:

\(\displaystyle \sqrt[n]{a^m}=a^{\frac{m}{n}}\) where \(n\in\mathbb{N}\) (this means \(n\) is a natural number, or positive integer.)
 

Clydey

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Converting from radical to exponential form, we use:

\(\displaystyle \sqrt[n]{a^m}=a^{\frac{m}{n}}\) where \(n\in\mathbb{N}\) (this means \(n\) is a natural number, or positive integer.)
Thanks for the insight. Much appreciated.
 

Otis

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... Presumably the index would be inside the v portion of the radical symbol?
Yes, that's where the index is shown.

When a radical expression displays no index, then the index is 2. In other words, a radical symbol with no index shown means square-root.



A side note: Be careful when handwriting radicals followed by a factor, to be sure it's clear what the radicand is (i.e., the expression inside the radical sign).

Even when properly formatted in printed material, I continue to see students read \(\sqrt{2}x\) as \(\sqrt{2x}\). With such expressions, I've gotten into the habit of always including explicit multiplication notation.

\(\sqrt{2} \cdot x\;\) or \(\; \sqrt{2}\;(x) \;\) or some such.

In fact, avoiding confusion could be the very reason why that author wrote \(x\sqrt{2}\). Cheers

😎
 

pka

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\sqrt[m]{x^n} wrapped in [_tex][/tex](remove the _) gives \(\displaystyle \sqrt[m]{x^n}\)
 

MarkFL

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\sqrt[m]{x^n} wrapped in [_tex][/tex](remove the _) gives \(\displaystyle \sqrt[m]{x^n}\)
You can wrap whatever you don't want to be parsed as BBCodes in PLAIN tags, for example:

[plain][MATH]\sqrt[m]{x^n}[/MATH][/plain]

This way, you can show users exactly what to post, as it renders thusly:

[MATH]\sqrt[m]{x^n}[/MATH]
 

topsquark

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Hmmm.. the noparse tag doesn't work here.

-Dan
 

mmm4444bot

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You can wrap whatever you don't want to be parsed as BBCodes in PLAIN tags ...
Good example, Mark. For other members, the new no-parse feature and other helpful information can be found in this thread. Cheers

😎
 

MarkFL

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topsquark

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Are you using [plain] and [/plain]?

😎
I thanked that post but for some reason forgot about it. I was using noparse instead of plain.

-Dan
 

Otis

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topsquark

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Maybe you suffer from CRS, like I do.

;)
A "Career Retention Specialist?" Actually, as it happens my high school gym teacher was a real schmuck. I found out years later that he was in the Marines and was a DSI... "Drill Sergeant Instructor." He's the guy that makes the drill sergeants so nasty. I now figure we got off easy in gym class.

Seriously though. I found a number of possibilities for CRS and none of them looked nice. Makes my PTSD seem like a toy.

-Dan
 
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