how do i simplify

sqrt[5+ssqrt(3)]

√(5+√3) ≈ 2.5946 ...

other than that, I can't think of a simpler algebraic expression.

can these help us ?

√a+√b?

not sure what you're getting at

You can play around with ideas like
√(4 + 2√3) = √(1 + 2√3 + 3) = √(1 + √3)^2 = 1+√3

like

√a+√b=√[(a+b)+2√ab)]

also true. I don't see that working here, however.

actually this is the actually question

2√[5+√3)]/(3√5-√3)

Still messy. You sure it wasn't just

2(√5+√3)/(3(√5-√3)) = 2/3 (√5+√3)^2 / (5-3) = (8+2√15)/3
or something?