Directions: Insert the indicated number of geometric means. Show your complete solution. 1. 16 and 81

To find the geometric mean between 16 and 81, we can use the formula for the geometric mean of two numbers: \[ \text{Geometric Mean} = \sqrt{a \times b} \] where \( a \) and \( b \) are the two numbers. Given: \( a = 16 \) \( b = 81 \) Substitute the values into the formula: \[ \text{Geometric Mean} = \sqrt{16 \times 81} \] Now, calculate the geometric mean: Calculate the value by following steps: - step0: Calculate: \(\sqrt{16\times 81}\) - step1: Multiply the numbers: \(\sqrt{1296}\) - step2: Write in exponential form: \(\sqrt{36^{2}}\) - step3: Simplify the root: \(36\) The geometric mean between 16 and 81 is 36.