PinkSapphire
  • PinkSapphire
Simplify by rationalizing the denominator.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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blackstreet23
  • blackstreet23
Pardon me but simplify which fraction?
PinkSapphire
  • PinkSapphire
\[\frac{ \sqrt{11} }{ 5\sqrt{132} }\]
PinkSapphire
  • PinkSapphire
Sorry, my internet is really slow today.

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PinkSapphire
  • PinkSapphire
@blackstreet23
PinkSapphire
  • PinkSapphire
For my answer, am I supposed to get rid of the square root in the denominator?
blackstreet23
  • 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
  • blackstreet23
example \[1/\sqrt{2} \]
PinkSapphire
  • PinkSapphire
I think I did that, but I'm not sure that I understood you completely.
blackstreet23
  • blackstreet23
hold on
blackstreet23
  • 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
  • blackstreet23
that is the same as multiplying by one
blackstreet23
  • blackstreet23
so you are not really changing the fraction itself, just how it looks
blackstreet23
  • blackstreet23
is like if you get a hair cut, you may change how you look but you are still the same person.
blackstreet23
  • blackstreet23
does that help a little?
blackstreet23
  • blackstreet23
what have you done so far?
PinkSapphire
  • PinkSapphire
Okay, I think I did that.
blackstreet23
  • blackstreet23
\[\frac{1 }{ \sqrt{2} } * \frac{ \sqrt{2} }{ \sqrt{2} }\]
blackstreet23
  • blackstreet23
ohh ok.
blackstreet23
  • blackstreet23
is that the answer on the back of the book?
PinkSapphire
  • PinkSapphire
What book?
blackstreet23
  • 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
  • PinkSapphire
Well, it is from my math book but we don't have the answers in the book.
PinkSapphire
  • 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
  • blackstreet23
ohh just go to equation on the bottom of the text rectangle it has the sigma sign\[\sum_{}^{}\]
blackstreet23
  • 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
  • PinkSapphire
On the phone it doesn't have that.
blackstreet23
  • blackstreet23
Could you use your phone as a hotspot so you use the phone's internet on your laptop?
blackstreet23
  • blackstreet23
anyway, just write what you have using root(#)
blackstreet23
  • blackstreet23
i will get it
PinkSapphire
  • PinkSapphire
I think I'll try it on the Safari app instead of the OpenStudy app.
PinkSapphire
  • PinkSapphire
I think I'll try it on the Safari app instead of the OpenStudy app.
PinkSapphire
  • PinkSapphire
No, it doesn't have it on there either.
PinkSapphire
  • PinkSapphire
It's working! Okay, this is the answer that I got:\[\frac{ \sqrt{11} }{ 10\sqrt{33} }\]
blackstreet23
  • blackstreet23
just write it how i told you. I will try to get it :D
blackstreet23
  • blackstreet23
ohh ok
PinkSapphire
  • PinkSapphire
Did you get a different answer?
blackstreet23
  • blackstreet23
that is perfect so far
blackstreet23
  • blackstreet23
but still incomplete
blackstreet23
  • blackstreet23
you can factor it a little bit more
blackstreet23
  • blackstreet23
what are the factors of 33?
PinkSapphire
  • PinkSapphire
3 and 11?
blackstreet23
  • blackstreet23
yes. so what could cancel?
PinkSapphire
  • PinkSapphire
\[\sqrt{11}\]
PinkSapphire
  • PinkSapphire
Right?
blackstreet23
  • blackstreet23
yes
blackstreet23
  • blackstreet23
so what are you left with?
PinkSapphire
  • PinkSapphire
\[10\sqrt{3}\]
PinkSapphire
  • PinkSapphire
Right?
blackstreet23
  • blackstreet23
actually \[1/10\sqrt{3}\]
blackstreet23
  • blackstreet23
but yes
blackstreet23
  • blackstreet23
and the last step is to do what i told you previously
PinkSapphire
  • PinkSapphire
Oh yeah, my mistake.
blackstreet23
  • blackstreet23
make a fraction with the rational in the denominator of the first fraction. That fraction must equal to 1
PinkSapphire
  • PinkSapphire
I don't understand.
blackstreet23
  • blackstreet23
which is the rational on the denominator of the fraction you have now?
PinkSapphire
  • PinkSapphire
\[\sqrt{3}\]
blackstreet23
  • blackstreet23
so take that rational and make a fraction that equals 1
blackstreet23
  • blackstreet23
do you know how to do it?
blackstreet23
  • blackstreet23
\[\frac{ 5 }{ 5 }\]
blackstreet23
  • blackstreet23
rings a bell?
PinkSapphire
  • PinkSapphire
How did you do that?
blackstreet23
  • blackstreet23
ohh no i was just showing you that any number over itself equals one
blackstreet23
  • blackstreet23
K/K = 1
blackstreet23
  • blackstreet23
k = constant
blackstreet23
  • blackstreet23
or any polynomial
blackstreet23
  • blackstreet23
over itself is equal to 1
blackstreet23
  • blackstreet23
so lets say
blackstreet23
  • blackstreet23
\[\frac{ \sqrt{3} }{ \sqrt{3} } = 1\]
PinkSapphire
  • PinkSapphire
Okay...
blackstreet23
  • 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
  • blackstreet23
you get it?
PinkSapphire
  • PinkSapphire
Not really. I'm sorry, but can you show it to me with numbers?
blackstreet23
  • blackstreet23
you mean the concept that every number over itself equal 1 or how to finish your problem?
PinkSapphire
  • PinkSapphire
How to finish my problem.
blackstreet23
  • blackstreet23
just multiply \[\frac{ \sqrt{3} }{ \sqrt{3} } * (previous fraction)\]
blackstreet23
  • blackstreet23
that is what i meant
mathstudent55
  • mathstudent55
|dw:1441502937030:dw|
blackstreet23
  • blackstreet23
\[\frac{ \sqrt{3} }{\sqrt{3} } * \frac{ \sqrt{1} }{ 10\sqrt{3} }\]
blackstreet23
  • blackstreet23
yes exactly
mathstudent55
  • mathstudent55
\(\dfrac{ \sqrt 3 }{\sqrt 3 } \times \dfrac{ \color{red}{1} }{ 10\sqrt 3 }\)
blackstreet23
  • 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
  • mathstudent55
You can also do it this way. |dw:1441503409900:dw|
blackstreet23
  • blackstreet23
yes that is the answer \[\frac{ \sqrt{3} }{ 30 }\]
PinkSapphire
  • PinkSapphire
Okay, I get it. Thanks @blackstreet23 and @mathstudent55
blackstreet23
  • blackstreet23
No problem, here to help :) good luck !
mathstudent55
  • mathstudent55
You're welcome.
PinkSapphire
  • PinkSapphire
Thanks for taking the time to help me! :)

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