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# what is 121^-1/2 as a surd

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121^-1/2 as a surd

Guest Aug 20, 2017
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#1
+178
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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
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Or, since indices comes before division:

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

Melody  Aug 20, 2017
#3
+4478
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Hmm...I have a question....What is a surd?

hectictar  Aug 20, 2017
#4
+178
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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
+90160
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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
+1

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

Then that makes the answer absurd

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

Guest Aug 20, 2017

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