Question

How to solve:

[(√2 + √6)/4]² / [(3√2) /8]

Answer 1

\[\LARGE \cfrac{\left(\cfrac{\sqrt2 +\sqrt6}{4}\right)^2}{\cfrac{3\sqrt2}{8}}\] are we talking about this ? :)

Answer 2

@Open2study ... is this what you mean :) ?

Answer 3

Nice... so first you have to split square in numerator and denominator...:
\[\LARGE \cfrac{\cfrac{( \sqrt2 +\sqrt6)^2} {4^2}}{\cfrac{3\sqrt2}{8}}\]
once you do that now you are supposed to know this formula:
\[\Large (a+b)^2=a^2+2ab+b^2\]
you have \[\LARGE (\sqrt2 +\sqrt6)^2\] try do it.. and tell me what you get :) (if you can't do it ...just let me know) :)

Answer 4

hmm... not exact number.. we have to do more work, we don't want to involve calculator now ;) ....

Answer 5

\[\LARGE (\sqrt2)^2+2\cdot \sqrt2 \cdot \sqrt6 +(\sqrt6)^2\]
\[\LARGE 2+2\cdot \sqrt2 \cdot \sqrt6 +6\]
\[\LARGE 8+2\cdot \sqrt2 \cdot \sqrt6 \] is this what you got ?

Answer 6

ok .. nice, now as we have multiply between two squares we can go like this:
\[\LARGE \sqrt a \cdot \sqrt b=\sqrt{a\cdot b}\]
in your case you have:
\[\LARGE \sqrt2 \cdot \sqrt6=\sqrt{?}\]
what should you get there? :)

Answer 7

two square roots :) .. sorry I made a typing mistake :F

Answer 8

whoaa.. I didn't think you're so smart . Sweet we just passed a big part ;) .. now let's get back to the begining...
as we had:
\[\LARGE \cfrac{\cfrac{( \sqrt2 +\sqrt6)^2} {4^2}}{\cfrac{3\sqrt2}{8}}\]
we've become like:
\[\LARGE \cfrac{\cfrac{( 8+2\cdot 2\sqrt3)} {16}}{\cfrac{3\sqrt2}{8}}\]
didn't we? ... is there anything you don't understand ?

Answer 9

Nice .. now there's something we can multiply between we continue...
\[\LARGE \cfrac{\cfrac{( 8+2\cdot 2\sqrt{3})} {16}}{\cfrac{3\sqrt2}{8}}\]
we multiply 2*2=4
\[\LARGE \cfrac{\cfrac{( 8+4\sqrt{3})} {16}}{\cfrac{3\sqrt2}{8}}\]
are we good till here? :)

Answer 10

ok .. now tell me . Example: if you have this fraction:
\[\LARGE \cfrac{\cfrac{2}{3}}{\cfrac45}=\] how would you deal with it? .. do you know how ? :)

Answer 11

Im not sure, can you teach me please?

Answer 12

Sure.. :) .. I'll draw something, If it's UGLY don't laugh lol :P

Answer 13

Im the worst at drawing lol

Answer 14

so it goes the numerator of the first fractions multiplies the denominator of the fraction down. and it appears in the numerator of the new fraction... and denominator of upper fraction multiplies the numerator of the fraction down and it appears as denominator of the new fraction... Example:
so if we have a fraction: Example:
\[\LARGE \cfrac{\cfrac ab}{\cfrac cd}=\cfrac{a\cdot d}{b\cdot c}\] do you understand? :) ,,, if you don't just let me know.