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Mathematics 7 Online
OpenStudy (anonymous):

Last one:

OpenStudy (anonymous):

\[\LARGE \frac{ 8 }{ 3 + \sqrt{2} }\]

hartnn (hartnn):

multiply and divide by 3-\(\sqrt 2\)

hartnn (hartnn):

then use \(\huge (a+b)(a-b)=a^2-b^2\)

OpenStudy (anonymous):

\[\large A) \frac{ 8\sqrt{2} }{ 5 }\] \[\large B) \frac{8\sqrt{2} }{ 3\sqrt{2} + 2}\] \[\large C) \frac{ 24-8\sqrt{2} }{ 7 }\] \[\large D) \frac{ 24-\sqrt{2} }{ 7 }\]

OpenStudy (anonymous):

Wait, multiply & divide what to what?

hartnn (hartnn):

\(\huge \LARGE \frac{ 8 }{ 3 + \sqrt{2} } \times \frac{3-\sqrt 2}{3-\sqrt 2}\)

OpenStudy (anonymous):

hmm....

hartnn (hartnn):

use this for denominator \(\huge (a+b)(a-b)=a^2-b^2\)

hartnn (hartnn):

a=3, b= \(\sqrt 2\)

OpenStudy (anonymous):

okay. so 3+sqrrt2 = ????

hartnn (hartnn):

what ? \((3+\sqrt 2)(3-\sqrt 2)=3^2-(\sqrt 2)^2=?\)

OpenStudy (anonymous):

Yeah, I was doing it piece by piece & then was going to multiply it all together & everything afterwards, haha. Sorry.

hartnn (hartnn):

\(\large (3+\sqrt 2)(3-\sqrt 2)=3^2-(\sqrt 2)^2=?\)

OpenStudy (anonymous):

umm, \[\Large 3\sqrt[2]{2}\] ????

OpenStudy (anonymous):

I don't know how to find that answer...

hartnn (hartnn):

3^2 = ?

OpenStudy (anonymous):

27

hartnn (hartnn):

wow!

OpenStudy (anonymous):

What?

hartnn (hartnn):

3^2 = 3*3 = ?

OpenStudy (anonymous):

oooh, sorry. 9

OpenStudy (anonymous):

i was thinking 3^3. My brain's not with it today.

hartnn (hartnn):

\(\huge \sqrt 2^2 = 2^{(1/2) *2}=?\)

OpenStudy (anonymous):

1

OpenStudy (anonymous):

?

hartnn (hartnn):

\(\huge \sqrt 2^2 = 2^{(1/2) *2}=2^1=?\)

OpenStudy (anonymous):

2

hartnn (hartnn):

so \(\large (3+\sqrt 2)(3-\sqrt 2)=3^2-(\sqrt 2)^2=?\)

OpenStudy (anonymous):

2?

OpenStudy (anonymous):

Oh, no 9-2, right?

hartnn (hartnn):

yes.

OpenStudy (anonymous):

Which equals 7. So the denominator is 7. Right?

hartnn (hartnn):

yes

OpenStudy (anonymous):

So, what do we do with the 8?

hartnn (hartnn):

8(3-\(\sqrt 2\))=?

OpenStudy (anonymous):

I don't know..

hartnn (hartnn):

8*3= ?

OpenStudy (anonymous):

24

hartnn (hartnn):

so 24-8\(\sqrt 2\)

OpenStudy (anonymous):

Ooooh, okay.

OpenStudy (anonymous):

Thank you :D

hartnn (hartnn):

welcome ^_^

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