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^{\frac{1}{2}}3⋅3
2
1
​

+6⋅3
2
1
​


18\cdot3^{\frac{1}{2}}18⋅3
2
1
​