`[(sqrt(2))^(3)]^(5/2)=(sqrt(2))^(2a+1)` then find `a`

If a=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) and b=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) then find a^(2)+b^(2)-5ab

If a=(2+sqrt(5))/(2-sqrt(5)) and b=(2-sqrt(5))/(2+sqrt(5)) then find value of a+b and b=(2-sqrt(5))/(2+sqrt(5)) then find

If x =(sqrt(5)-2)/(sqrt(5)+2) and y = (sqrt(5)+2)/(sqrt(5)-2) : find : xy

If x=(sqrt5+sqrt2)/(sqrt5-sqrt2) and y=(sqrt5-sqrt2)/(sqrt5+sqrt2) then find the value of (3x-2y)(x+2y)

If x = (sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2)) , find the value of x^(2) + (1)/(x^(2)) .

If a=(sqrt(5)+sqrt(2))/(sqrt(5)-sqrt(2)) and b=(sqrt(5)-sqrt(2))/(sqrt(5)+sqrt(2)), find the value of (a^(2)+ab+b^(2))/(a^(2)-ab+b^(2))

If (sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))=3 then x=1)sqrt((2)/(3)2)sqrt((1)/(3))3)sqrt((2)/(5))sqrt((3)/(5))

If x=((sqrt(5)-2))/(sqrt(5)+2) and y=(sqrt(5)+2)/(sqrt(5)-2) find (i)

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))