Simplify by rationalizing the denominator.

- PinkSapphire

Simplify by rationalizing the denominator.

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- blackstreet23

Pardon me but simplify which fraction?

- PinkSapphire

\[\frac{ \sqrt{11} }{ 5\sqrt{132} }\]

- PinkSapphire

Sorry, my internet is really slow today.

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## More answers

- PinkSapphire

@blackstreet23

- PinkSapphire

For my answer, am I supposed to get rid of the square root in the denominator?

- blackstreet23

ohh ok well for rationalyze you just need to multiply the fraction by the number on the denominator as a fraction so it equals to one

- blackstreet23

example \[1/\sqrt{2} \]

- PinkSapphire

I think I did that, but I'm not sure that I understood you completely.

- blackstreet23

hold on

- blackstreet23

so yeah to rationalize that you would have to multiply the previous fraction by the number in the denominator as a fraction
I mean
\[\sqrt{2}/\sqrt{2}\]

- blackstreet23

that is the same as multiplying by one

- blackstreet23

so you are not really changing the fraction itself, just how it looks

- blackstreet23

is like if you get a hair cut, you may change how you look but you are still the same person.

- blackstreet23

does that help a little?

- blackstreet23

what have you done so far?

- PinkSapphire

Okay, I think I did that.

- blackstreet23

\[\frac{1 }{ \sqrt{2} } * \frac{ \sqrt{2} }{ \sqrt{2} }\]

- blackstreet23

ohh ok.

- blackstreet23

is that the answer on the back of the book?

- PinkSapphire

What book?

- blackstreet23

you did not take this question from a math book? ohh is ok then. I was just wondering so i made sure you had 100% the right answer

- PinkSapphire

Well, it is from my math book but we don't have the answers in the book.

- PinkSapphire

Right now my laptop is really slow so I'm using my phone but I don't know how to type my answer in because of the radical signs.

- blackstreet23

ohh just go to equation on the bottom of the text rectangle it has the sigma sign\[\sum_{}^{}\]

- blackstreet23

and i just asked because in all my math books we always have the answers so we know we are doing it right haha

- PinkSapphire

On the phone it doesn't have that.

- blackstreet23

Could you use your phone as a hotspot so you use the phone's internet on your laptop?

- blackstreet23

anyway, just write what you have using root(#)

- blackstreet23

i will get it

- PinkSapphire

I think I'll try it on the Safari app instead of the OpenStudy app.

- PinkSapphire

I think I'll try it on the Safari app instead of the OpenStudy app.

- PinkSapphire

No, it doesn't have it on there either.

- PinkSapphire

It's working! Okay, this is the answer that I got:\[\frac{ \sqrt{11} }{ 10\sqrt{33} }\]

- blackstreet23

just write it how i told you. I will try to get it :D

- blackstreet23

ohh ok

- PinkSapphire

Did you get a different answer?

- blackstreet23

that is perfect so far

- blackstreet23

but still incomplete

- blackstreet23

you can factor it a little bit more

- blackstreet23

what are the factors of 33?

- PinkSapphire

3 and 11?

- blackstreet23

yes. so what could cancel?

- PinkSapphire

\[\sqrt{11}\]

- PinkSapphire

Right?

- blackstreet23

yes

- blackstreet23

so what are you left with?

- PinkSapphire

\[10\sqrt{3}\]

- PinkSapphire

Right?

- blackstreet23

actually \[1/10\sqrt{3}\]

- blackstreet23

but yes

- blackstreet23

and the last step is to do what i told you previously

- PinkSapphire

Oh yeah, my mistake.

- blackstreet23

make a fraction with the rational in the denominator of the first fraction. That fraction must equal to 1

- PinkSapphire

I don't understand.

- blackstreet23

which is the rational on the denominator of the fraction you have now?

- PinkSapphire

\[\sqrt{3}\]

- blackstreet23

so take that rational and make a fraction that equals 1

- blackstreet23

do you know how to do it?

- blackstreet23

\[\frac{ 5 }{ 5 }\]

- blackstreet23

rings a bell?

- PinkSapphire

How did you do that?

- blackstreet23

ohh no i was just showing you that any number over itself equals one

- blackstreet23

K/K = 1

- blackstreet23

k = constant

- blackstreet23

or any polynomial

- blackstreet23

over itself is equal to 1

- blackstreet23

so lets say

- blackstreet23

\[\frac{ \sqrt{3} }{ \sqrt{3} } = 1\]

- PinkSapphire

Okay...

- blackstreet23

and that is what you would have to multiply so you are not actually altering the fraction, just changing how it looks :P

- blackstreet23

you get it?

- PinkSapphire

Not really. I'm sorry, but can you show it to me with numbers?

- blackstreet23

you mean the concept that every number over itself equal 1 or how to finish your problem?

- PinkSapphire

How to finish my problem.

- blackstreet23

just multiply \[\frac{ \sqrt{3} }{ \sqrt{3} } * (previous fraction)\]

- blackstreet23

that is what i meant

- mathstudent55

|dw:1441502937030:dw|

- blackstreet23

\[\frac{ \sqrt{3} }{\sqrt{3} } * \frac{ \sqrt{1} }{ 10\sqrt{3} }\]

- blackstreet23

yes exactly

- mathstudent55

\(\dfrac{ \sqrt 3 }{\sqrt 3 } \times \dfrac{ \color{red}{1} }{ 10\sqrt 3 }\)

- blackstreet23

yes you are right @mathstudent55 even though is the same thing haha i mean 1 and root (1), but yeah for clarity just 1 is better

- mathstudent55

You can also do it this way.
|dw:1441503409900:dw|

- blackstreet23

yes that is the answer \[\frac{ \sqrt{3} }{ 30 }\]

- PinkSapphire

Okay, I get it. Thanks @blackstreet23 and @mathstudent55

- blackstreet23

No problem, here to help :) good luck !

- mathstudent55

You're welcome.

- PinkSapphire

Thanks for taking the time to help me! :)

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