`(sqrt5-sqrt2)(sqrt5+sqrt2)`

Find : (sqrt5+sqrt2)(sqrt3+sqrt2)

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

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

solve (3sqrt5 +sqrt3)/(sqrt5 -sqrt3)

Simplify each of the following expressions: (i) (3+sqrt(3))(2+sqrt(2)) (ii) (3+sqrt(3))(3-sqrt(3)) (iii) (sqrt(5)+sqrt(2))^2 (iv) (sqrt(5)-sqrt(2))(sqrt(5)+sqrt(2))

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

Simplify (7sqrt3)/(sqrt10+sqrt3)-(2sqrt5)/(sqrt6+sqrt5)-(3sqrt2)/(sqrt15+3sqrt2)

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):}|

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

Simplify the following expressions: (i) (3+sqrt(3))\ (3-sqrt(3)) (ii) (sqrt(5)-\ sqrt(2)\ )(sqrt(5)+sqrt(2))