Question

Simplify by rationalizing the denominator.

Answer 1

Pardon me but simplify which fraction?

Answer 2

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

Answer 3

Sorry, my internet is really slow today.

Answer 4

@blackstreet23

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

hold on

Answer 10

so yeah to rationalize that you would have to multiply the previous fraction by the number in the denominator as a fraction

I mean

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

Answer 11

that is the same as multiplying by one

Answer 12

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

Answer 13

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

Answer 14

does that help a little?

Answer 15

what have you done so far?

Answer 16

Okay, I think I did that.

Answer 17

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

Answer 18

ohh ok.

Answer 19

is that the answer on the back of the book?

Answer 20

What book?

Answer 21

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

Answer 22

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

Answer 23

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.

Answer 24

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

Answer 25

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

Answer 26

On the phone it doesn't have that.

Answer 27

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

Answer 28

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

Answer 29

i will get it

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

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

Answer 35

ohh ok

Answer 36

Did you get a different answer?

Answer 37

that is perfect so far

Answer 38

but still incomplete

Answer 39

you can factor it a little bit more

Answer 40

what are the factors of 33?

Answer 41

3 and 11?

Answer 42

yes. so what could cancel?

Answer 43

\[\sqrt{11}\]

Answer 44

Right?

Answer 45

yes

Answer 46

so what are you left with?

Answer 47

\[10\sqrt{3}\]

Answer 48

Right?

Answer 49

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

Answer 50

but yes

Answer 51

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

Answer 52

Oh yeah, my mistake.

Answer 53

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

Answer 54

I don't understand.

Answer 55

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

Answer 56

\[\sqrt{3}\]

Answer 57

so take that rational and make a fraction that equals 1

Answer 58

do you know how to do it?

Answer 59

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

Answer 60

rings a bell?

Answer 61

How did you do that?

Answer 62

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

Answer 63

K/K = 1

Answer 64

k = constant

Answer 65

or any polynomial

Answer 66

over itself is equal to 1

Answer 67

so lets say

Answer 68

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

Answer 69

Okay...

Answer 70

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

Answer 71

you get it?

Answer 72

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

Answer 73

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

Answer 74

How to finish my problem.

Answer 75

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

Answer 76

that is what i meant