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!

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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)   (Show Source): You can put this solution on YOUR website!
Here's one way to do it


Start with the given expression.


Combine the roots using the identity


Reduce the fraction.


Break up the fraction using the identity (ie it's the reverse of the other identity)


Take the square root of 1 to get 1.


Take the square root of 36 to get 6.


So



==========================================================================

Or...

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


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 . We must do the same for the numerator as well.

Multiply both the numerator and denominator by


------------------------------------------

Scratch Work


Take note that since (it's like those previous identities). Since , we can say that .

For the last step of that equation, the square root 'undoes' the square. In other words, where


In the end,

------------------------------------------

Now back to the problem at hand....


Multiply with to get 180 (see scratch work above).



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More Scratch Work

Following the same idea, due to the identity .

So

In the end,


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

------------------------------------------

Now back to the problem at hand....


Multiply with to get 30 (see scratch work above).


Reduce the fraction.


So regardless of the method used to get the answer.

Answer by edjones(8007)   (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

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