How do you simplify 2 / (5 - sqrt 2)?

1 Answer
Alan P.
Oct 24, 2015

2/(5-sqrt(2)) = (10+2sqrt(2))/23

Explanation:

We can rationalize the denominator by multiplying it (and the numerator) by the conjugate of the denominator.

2/(5-sqrt(2))
color(white)("XXX")=2/(5-sqrt(2)) xx (5+sqrt(2))/(5+sqrt(2))

color(white)("XXX")=(10+2sqrt(2))/(5^2-(sqrt(2))^2)

color(white)("XXX")=(10+2sqrt(2))/23

(Some people would consider this "simpler").

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