Mathematics
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OpenStudy (anonymous):
Last one:
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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?
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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 = ????
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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...
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hartnn (hartnn):
3^2 = ?
OpenStudy (anonymous):
27
hartnn (hartnn):
wow!
OpenStudy (anonymous):
What?
hartnn (hartnn):
3^2 = 3*3 = ?
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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):
?
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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?
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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-\(\sqrt 2\))=?
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OpenStudy (anonymous):
I don't know..
hartnn (hartnn):
8*3= ?
OpenStudy (anonymous):
24
hartnn (hartnn):
so 24-8\(\sqrt 2\)
OpenStudy (anonymous):
Ooooh, okay.
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OpenStudy (anonymous):
Thank you :D
hartnn (hartnn):
welcome ^_^