SOLUTION: I am struggling with this one ....any help is much appreciated! Simplify Square root of 5 over the square root of 180 Thank you!

Algebra ->  Square-cubic-other-roots -> SOLUTION: I am struggling with this one ....any help is much appreciated! Simplify Square root of 5 over the square root of 180 Thank you!      Log On


   

Question 249026: I am struggling with this one ....any help is much appreciated!
Simplify
Square root of 5 over the square root of 180
Thank you!
Found 2 solutions by jim_thompson5910, edjones:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Here's one way to do it


sqrt%285%29%2Fsqrt%28180%29 Start with the given expression.


sqrt%285%2F180%29 Combine the roots using the identity sqrt%28x%29%2Fsqrt%28y%29=sqrt%28x%2Fy%29


sqrt%281%2F36%29 Reduce the fraction.


sqrt%281%29%2Fsqrt%2836%29 Break up the fraction using the identity sqrt%28x%2Fy%29=sqrt%28x%29%2Fsqrt%28y%29 (ie it's the reverse of the other identity)


1%2Fsqrt%2836%29 Take the square root of 1 to get 1.


1%2F6 Take the square root of 36 to get 6.


So sqrt%285%29%2Fsqrt%28180%29=1%2F6



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Or...

Here's another way to do it. This method is more common as it works better in general.


sqrt%285%29%2Fsqrt%28180%29 Start with the given expression.


The goal is to get the denominator equal to a rational number. To do this, we multiply the denominator by sqrt%28180%29. We must do the same for the numerator as well.

%28sqrt%285%29%2Asqrt%28180%29%29%2F%28sqrt%28180%29%2Asqrt%28180%29%29 Multiply both the numerator and denominator by sqrt%28180%29


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Scratch Work


Take note that sqrt%28180%29%2Asqrt%28180%29=sqrt%28180%2A180%29 since sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29 (it's like those previous identities). Since sqrt%28180%29%2Asqrt%28180%29=sqrt%28180%2A180%29, we can say that sqrt%28180%29%2Asqrt%28180%29=sqrt%28180%2A180%29=sqrt%28180%5E2%29=180.

For the last step of that equation, the square root 'undoes' the square. In other words, sqrt%28x%5E2%29=x where x%3E=0


In the end, sqrt%28180%29%2Asqrt%28180%29=180

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Now back to the problem at hand....


%28sqrt%285%29%2Asqrt%28180%29%29%2F180 Multiply sqrt%28180%29 with sqrt%28180%29 to get 180 (see scratch work above).



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More Scratch Work

Following the same idea, sqrt%285%29%2Asqrt%28180%29=sqrt%285%2A180%29 due to the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29.

So sqrt%285%29%2Asqrt%28180%29=sqrt%285%2A180%29=sqrt%28900%29=sqrt%2830%5E2%29=30

In the end, sqrt%285%29%2Asqrt%28180%29=30


If you're not sure about your work, a calculator will come in handy to check your work.

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Now back to the problem at hand....


30%2F180 Multiply sqrt%285%29 with sqrt%28180%29 to get 30 (see scratch work above).


1%2F6 Reduce the fraction.


So sqrt%285%29%2Fsqrt%28180%29=1%2F6 regardless of the method used to get the answer.

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(5)/sqrt(180)
=sqrt(5)/sqrt(36*5)
=sqrt(5)/6sqrt(5)
=1/6
.
Ed