Question 44608
Add the denominators because they have the same base of sqrt2
sqrt3 + sqrt5 / 5 sqrt2
 .
Rationalize the radical by multiplying the numerator and denominator by sqrt2:

(sqrt(3) + sqrt5) (sqrt2)/ (5 sqrt2)(sqrt2)
.
Distribute sqrt2 in the numerator.  In the denominator (sqrt2)(sqrt2)=2:
sqrt(3*2) + sqrt(5*2)/(5*2)
.
Simplify:
sqrt6 + sqrt10/10