Question

√2+√5
_______
---------
√2-√5

please show steps :)

Answer 1

See below.

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

Answer 2

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

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)

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

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

(7+2sqrt(10))

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

-3

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