Given \sqrt{27}+\sqrt{108} 27

+
108


=27^{\frac{1}{2}}+108^{\frac{1}{2}} =27
2
1


+108
2
1


3^{\frac{1}{2}}\cdot9^{\frac{1}{2}} +3^{\frac{1}{2}}\cdot36^{\frac{1}{2 }}3
2
1


⋅9
2
1


+3
2
1


⋅36
2
1


3\cdot3^{\frac{1}{2}}+6\cdot3^{\fra c{1}{2}}3⋅3
2
1


+6⋅3
2
1


18\cdot3^{\frac{1}{2}}18⋅3
2
1