equation that I need help with is 8 over 3 plus sqrt 7

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equation that I need help with is 8 over 3 plus sqrt 7

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[\frac{8}{3+\sqrt{7}}\]
is that it
well if it is multiply top and bottom by conjugate \[\frac{8}{3+\sqrt{7}}*\frac{3-\sqrt{7}}{3-\sqrt{7}}\] \[=\frac{24-8\sqrt{7}}{2}\] factor out a 2 on top which cancels the 2 on bottom leaving \[= 12-4\sqrt{7}\]

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Other answers:

wonderful! how did you come up with the 8, though? is it that you must include the same number you multiply with in the top equation?
and how in the heck did you get 2?
oh, never mind. thank you!
by distributing on top, FOIL on bottom your welcome :)
quick question- for these types of problems, will the denominator always be 2?

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