Question

√2+√5 _______ --------- √2-√5 please show steps :)

Answer 1

Answer:

-1/3 (7 + 2 sqrt(10))

Step-by-step explanation:

(sqrt(2)+sqrt(5))

-------------------

sqrt(2)- sqrt(5)

We need to multiply the top and bottom by the complex conjugate of the bottom.  The complex conjugate of the bottom is sqrt(2) + sqrt(5)

(sqrt(2)+sqrt(5)) * (sqrt(2)+sqrt(5)

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(sqrt(2)- sqrt(5)) * (sqrt(2)+sqrt(5))

FOILing the top and bottom

(2+sqrt(10) + sqrt(10)+5)

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(2- sqrt(10) +sqrt(10)-5)

(7+2sqrt(10))

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-3

-1/3 (7 + 2 sqrt(10))

Answer 2

Answer:

See below.

Step-by-step explanation:

You multiply top and bottom of the fraction by the conjugate of

√2-√5  which is √2+√5:

√2+√5               √2+√5    *   √2+√5          2 + 2√2√5  + 5

_______  =         _______________  =   ___________

√2-√5                √2-√5     *   √2+√5                  2 -  5

       - (7 + 2√10)

=     __________    Answer.

               3