Question

Rationalize the denominator.
sqrt2/sqrt2+sqrt5

Answer 1

I mean... {root(2) - root(5)}

Answer 2

okay, would be root4 + root10/2 + 5 ?

Answer 3

2+sqrt10/7 ?

Answer 4

in the answers section, it says the answer is 2-sqrt10/-3 . im not sure how they got that :/

Answer 5

\[\frac{\sqrt2}{\sqrt2-\sqrt5}\] Multiply by the conjugate (switch the middle sign) of the denominator over itself (since anything over itself = 1).

sqrt2(sqrt2-sqrt5) = (sqrt2)^2-(sqrt2)(sqrt5) = 2-sqrt10
(sqrt2-sqrt5)(sqrt2+sqrt5) = (sqrt2)^2-(sqrt5)^2 = 2-5 = -3

\[\frac{2-\sqrt10}{-3}\]

Answer 6

oooh. i didnt know i had to switch the middle sign. thanks!