+31 simplify in radiacal expression \(\sqrt{ \dfrac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5} + \sqrt{2} } } + \sqrt{ \dfrac{ \sqrt{5} + \sqrt{2} }{ \sqrt{5} - \sqrt{2} }} \,\)
+856 We want to simplify sqrt((sqrt(5) - sqrt(2))/(sqrt(5) + sqrt(2))) + sqrt((sqrt(5) + sqrt(2))/(sqrt(5) - sqrt(2)))
Rationalizing the denominator, we get sqrt((sqrt(5) - sqrt(2))^2) + sqrt((sqrt(5) + sqrt(2))^2
= sqrt(5) - sqrt(2) + sqrt(5) + sqrt(2)
= 2*sqrt(5).
The final answer is 2*sqrt(5).
+129820 Simplifying, we have
sqrt [ ( sqrt 5 - sqrt 2)^2 ] + sqrt [ (sqrt 5 + sqrt 2)^2 ]
___________________________________________ =
sqrt [ 5 - 2 ]
[ sqrt 5 - sqrt 2 ] + [ sqrt 5 + sqrt 2 ]
____________________________ =
sqrt 3
2sqrt 5
______ =
sqrt 3
(2/3) sqrt 15
