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

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Answer 1 · 2015-09-08T12:07:13

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

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

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

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

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

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

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