1 last square root :

Rationalize the denominator

5/sqrt[3]+sqrt[5]=

5*sqrt[3]-sqrt[5]/ sqrt[3]sqrt5[5]*sqrt[3]-sqrt[5]=

5sqrt[3]-5sqrt[5]/sqrt[9]-sqrt[15]+sqrt[15]- sqrt[25]=

5sqrt[3]-5sqrt[5]/-16 =

5sqrt[3]-5sqrt[5]/ -2

Rationalize the denominator

5/sqrt[3]+sqrt[5]=

5*sqrt[3]-sqrt[5]/ sqrt[3]sqrt5[5]*sqrt[3]-sqrt[5]=

5sqrt[3]-5sqrt[5]/sqrt[9]-sqrt[15]+sqrt[15]- sqrt[25]=

5sqrt[3]-5sqrt[5]/-16 =

5sqrt[3]-5sqrt[5]/ -2

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