Question

Rationalize the denominator of
https://api.agilixbuzz.com/Resz/~Ey6YBAAAAAA81ZXByil0iA.RBcymAkaS7gygkcdGLtgrA/19809088,B87/Assets/assessmentimages/alg%202%20pt%202%20u3l8%2011.jpg
@wolf1728
@thesmartone

Answer 1

@zzr0ck3r

Answer 2

@whpalmer4

Answer 3

multiply top and bottom by \(2+\sqrt{6}\)

Answer 4

is it 2-

Answer 5

@zzr0ck3r

Answer 6

i thought you multiply the denominator

Answer 7

\[4-\sqrt{6}\]
i got this for numerator but don't know what to do now @TheSmartOne

Answer 8

@agent0smith

Answer 9

@Zarkon

Answer 10

@pooja195

Answer 11

@Kainui

Answer 12

Describe to me what you did, and where your answer is so far.

Answer 13

i multiplied the denominator and numerator

Answer 14

@mjdennis

Answer 15

@Jaynator495

Answer 16

@rebeccaxhawaii

Answer 17

@zepdrix

Answer 18

@TheSmartOne

Answer 19

I don't understand "multiplied the denominator and numerator" Did you multiply them together? Did you multiply them both by one thing?

Answer 20

OK, let's start over.
Simplify
2 + √6
------
2 - √6

Right?

Answer 21

\[\frac{ 2+\sqrt{6} }{ 2-\sqrt{6} } \times \frac{ 2-\sqrt{6} }{ 2-\sqrt{6} }\]

Answer 22

OK, that was close. You really need to use 2 + √6. I think you will see why that is better when you do it

Answer 23

Sorry, I mean 2 + √6 on both top AND bottom. One sec, I will put it in the equation editor.

Answer 24

\[\frac{ 2+\sqrt{6} }{2-\sqrt{6} } \times \frac{ 2+\sqrt{6} }{2+\sqrt{6} }\]

Answer 25

ok so what do i do now?

Answer 26

@mjdennis

Answer 27

This is the same as: \[\frac{ (2+\sqrt{6}) \times (2+\sqrt{6}) }{ (2-\sqrt{6}) \times (2+\sqrt{6}) }\]

Answer 28

So do those two multiplications out

Answer 29

\[\frac{ 4+\sqrt{36} }{ 4-\sqrt{36} }\]

Answer 30

is that right?

Answer 31

The denominator is right. The numerator is the form (a+b)(a+b) = a^2+2ab+b^2, so try the numerator again,please.

Answer 32

im not really sure what that means?

Answer 33

it means when you multiply (2+√6)×(2+√6), you have to add _four_ terms:
(2×2)
(2×√6)
(√6 × 2)
(√6 × √6)
and add those up.

Answer 34

4
2sqrt6
2sqrt6
6

Answer 35

is that right?

Answer 36

Yes, but add them up.
You may want to practice multiplying mixed numbers (like 2+√6) some more.

Answer 37

Youw ill need that skill more in math.

Answer 38

Ha, sorry, "You will.."

Answer 39

@18jonea , I'll hang out a bit in case you come back.

Answer 40

im back sorry had to get a snack

Answer 41

NP. Gotta stay fueled up.

Answer 42

4.89897948557 i got this for 2 square root 6

Answer 43

Not sure how you are supposed to put the answer. Does the problem say?

Answer 44

I would have left the √6 alone in my answer.

Answer 45

o ok

Answer 46

Let's follow that through, just in case, then you also have that answer.

Answer 47

-5
-1
\[-5-2\sqrt{6}\]
\[-\frac{ 5 }{ 2}-\sqrt{6}\]

Answer 48

are my options

Answer 49

4+6 is 10, but I figure you got that part.
2√6 +2√6 is 4√6, right?
So the top is 10+√6

Answer 50

yes

Answer 51

The bottom was 4-√36 . Can you reduce that?

Answer 52

\[\sqrt{6}\]

Answer 53

sorry just 6

Answer 54

Did you mean 4-6? That reduces further still.

Answer 55

-2

Answer 56

Oops. Top should have been 10+4√6 I'll re do it

Answer 57

d?

Answer 58

Put them back together and we are almost done: \[\frac{ 10+4\sqrt{6} }{ -2 }\] and you can use distribution to split the -2 over both halves: \[\frac{ 10 }{ -2 } + \frac{ 4\sqrt{6} }{ -2 }\]
Can you bring it home? Only one match among your choices.

Answer 59

Not d

Answer 60

c

Answer 61

I guess. You didn't label the choices!

Answer 62

\[-5-2\sqrt{6}\]

Answer 63

@mjdennis

Answer 64

Wait, I helped you through all the tough stuff, and you would like me to believe that you cannot divide 10 by -2, or divide 4√6 by -2 , and be confident in the answer?

Answer 65

-5 is the 10

Answer 66

So, I think you got it from here.

Answer 67

just dont know the square root

Answer 68

im 99% sure it is c

Answer 69

OK. Right, 10/(-2) is -5. Only one answer had -5, so be confident in that.

When we write √6, we are using "√6" as a symbol. It stands in for an number a little bigger than 2.449 and a little smaller than 2.450. So we can just treat it as any other number, but leave it as a symbol.

Suppose I asked you to find 20/-2 ? You could say "20 is 2*10, and I know 10/-2 is -5, so 20/-2 is twice -5, so 20/-2 is -10. Same for 4√6/-2. It is =2√6. We never have to touch the √6, because it is the simplest form.

Answer 70

Good luck! Gotta go.