You can put this solution on YOUR website! Add the denominators because they have the same base of sqrt2
sqrt3 + sqrt5 / 5 sqrt2
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Rationalize the radical by multiplying the numerator and denominator by sqrt2:
(sqrt(3) + sqrt5) (sqrt2)/ (5 sqrt2)(sqrt2)
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Distribute sqrt2 in the numerator. In the denominator (sqrt2)(sqrt2)=2:
sqrt(3*2) + sqrt(5*2)/(5*2)
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Simplify:
sqrt6 + sqrt10/10