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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