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)
----------------------------------
(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))
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
