+0

+1
1
2
+31

simplify in radiacal expression $$\sqrt{ \dfrac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5} + \sqrt{2} } } + \sqrt{ \dfrac{ \sqrt{5} + \sqrt{2} }{ \sqrt{5} - \sqrt{2} }} \,$$

Jul 26, 2024

#2
+129806
+2

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

Jul 26, 2024

#1
+840
-2

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).

Jul 26, 2024
#2
+129806
+2

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

CPhill Jul 26, 2024