Show that $(\prod_{i=1}^{n} (a_i+b_i))^{\frac{1}{n}} \geq (\prod_{i=1}^{n} {a_i})^{\frac{1}{n}}+(\prod_{i=1}^{n} {b_i})^{\frac{1}{n}}$
Prove $(a_1+b_1)^{1/n}\cdots(a_n+b_n)^{1/n}\ge \left(a_1\cdots a_n\right)^{1/n}+\left(b_1\cdots b_n\right)^{1/n}$