`(sqrt5+sqrt3)(sqrt5-sqrt3)`

Simplify (sqrt5-sqrt2)(sqrt5+sqrt2)

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

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

Simplify: (i) (3sqrt(2)-2sqrt(2))/(3sqrt(2)+\ 2sqrt(3))+(sqrt(12))/(sqrt(3)-\ sqrt(2)) (ii) (sqrt(5)+\ sqrt(3))/(sqrt(5)-\ sqrt(3))+(sqrt(5)-\ sqrt(3))/(sqrt(5)+\ sqrt(3))

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))

If x=(sqrt(5)+\ sqrt(3))/(sqrt(5)-\ sqrt(3)) and y=(sqrt(5)-\ sqrt(3))/(sqrt(5)+\ sqrt(3)) , then x+y+x y= (a) 9 (b) 5 (c) 17 (d) 7

If both a\ a n d\ b are rational numbers, find the values of a\ a n d\ b in each of the following equalities: (sqrt(5)+\ sqrt(3))/(sqrt(5)-\ sqrt(3))=a+b\ sqrt(15)

Express the following in the form a+bi, where a and b are real numbers ((3 + sqrt5i) (3-sqrt5i))/((sqrt3+sqrt2i)- (sqrt3-sqrt2i))

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

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