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121^-1/2 as a surd

Guest Aug 20, 2017
 #1
avatar+178 
+1

Input: 121^-1/2 as a surd

Intepretation: Express the number \(121^{-\frac{1}{2}}\)

We apply the rule of exponentials:

\(a^\frac{n}{m}\)=\(\sqrt[m]{a^n}\)

And:

\(a^{-b}=\frac{1}{a^b}\)

Merge the two rules and we get:
\(a^{-\frac{n}{m}}=\frac{1}{\sqrt[m]{a^n}}\)

Now plug \(a=121,m=2,n=1\) into the equation above:

\(121^{-\frac{1}{2}}=\frac{1}{\sqrt[2]{121^1}}\)

Simplify:

\(=\frac{1}{\sqrt{121}}\)

\(=\frac{1}{11}\)

Done :D

Jeffes02  Aug 20, 2017
 #2
avatar+93305 
+1

Or, since indices comes before division:

 

\(\frac{121^{-1}}{2}=\frac{1}{2*121}=\frac{1}{242}\)

Melody  Aug 20, 2017
 #3
avatar+7266 
+2

Hmm...I have a question....What is a surd?

hectictar  Aug 20, 2017
 #4
avatar+178 
+2

Don't know what it means, either. I fact-checked the wikipedia and it seems to either be the short term for irrational numbers, or the nth-root of numbers. But this question is answered anyways :D

(Source: https://en.wikipedia.org/wiki/Surd)     -Disambiguation Page

Jeffes02  Aug 20, 2017
edited by Jeffes02  Aug 20, 2017
 #5
avatar+93305 
+2

A surd is a commonly used term used in Australia.

It means an irrational number that is under a square root. 

Maybe it applies to other roots other than 2 but I do not recall seeing it ever being used that way.

Usually it is the irrational square root of a positive integer.

 

So for this question it makes no sense as the answer is rational.

Melody  Aug 20, 2017
 #6
avatar
+1

. . . for this question it makes no sense as the answer is rational.

 

Then that makes the answer absurd laugh

https://web2.0calc.com/questions/which-of-the-following-is-not-a-surd

Guest Aug 20, 2017

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