How do you simplify # [sqrt2 + sqrt 5] / [sqrt2 – sqrt5]#?

1 Answer
Alan P.
Sep 8, 2015

#-(7+2sqrt(10))/3#

Explanation:

We can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator:

#(sqrt(2)+sqrt(5))/(sqrt(2)-sqrt(5))#

#=(sqrt(2)+sqrt(5))/(sqrt(2)-sqrt(5))xx(sqrt(2)+sqrt(5))/(sqrt(2)+sqrt(5))#

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

#=-(7+2sqrt(10))/3#

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