The geometric mean of a set with n elements is given by
[tex]g=\sqrt[n]{x_1\cdot x_2\cdot...\cdot x_n}[/tex]In our problem, we have only two elements, therefore, we have n = 2. The geometric mean between 5 and 20 is
[tex]g=\sqrt[]{5\cdot20}=\sqrt[]{100}=10[/tex]