`2sqrt5 - sqrt5 = sqrt5`

If x= ( sqrt5- sqrt3)/ ( sqrt5+ sqrt3) and y= ( sqrt5+ sqrt3)/( sqrt5- sqrt3) find the value of x^(2) + y ^(2)

(sqrt5 - sqrt3)/(sqrt5 + sqrt3) is equal to :

Simplify : (\sqrt 5 - \sqrt 3)/(\sqrt 3 + \sqrt 5) \times (\sqrt 5 - \sqrt 3)/(\sqrt 3 -\sqrt 5)

Simplify: (sqrt 3 - sqrt 5)(sqrt 5+ sqrt 3)

Find (sqrt 3 - sqrt 5)(sqrt 5+ sqrt3)

Find the value of determinant |sqrt((13))+sqrt(3)2sqrt(5)sqrt(5)sqrt((15))+sqrt((26))5sqrt((10))3+sqrt((65))sqrt((15))5|

Using the properties of detminants, evalulate. (i) |{:(,23,6,11),(,36,5,26),(,63,13,37):}| (ii) |{:(,sqrt13+sqrt3,2sqrt5,sqrt5),(,sqrt15+sqrt26,5,sqrt10),(,3+sqrt65,sqrt15,5):}|

(iii) (sqrt 5+ sqrt 3)/(sqrt5-sqrt3)+(sqrt5-sqrt3)/(sqrt5+sqrt3) =?

Find the value of the "determinant" |{:(sqrt13+sqrt3,2sqrt5,sqrt5),(sqrt26+sqrt15,5,sqrt10),(sqrt65+3,sqrt15,5):}|

The value of |{:(sqrt(13 )+ sqrt(3), 2sqrt(5),sqrt(5)),(sqrt(15) + sqrt(26),5,sqrt(10)),(3 + sqrt(65), sqrt(15),5):}|