A) Find the geometric mean for each pair \( \begin{array}{lll}\text { 1) } \frac{1}{3}, 32 & \text { 2) } 5,10 & \text { 3) } 624\end{array} \)

The geometric mean of two numbers \( a \) and \( b \) is calculated using the formula: \[ \text{Geometric Mean} = \sqrt{a \cdot b} \] Now, let's calculate the geometric mean for each pair: 1) For the pair \( \frac{1}{3} \) and \( 32 \): \[ \text{Geometric Mean} = \sqrt{\frac{1}{3} \cdot 32} = \sqrt{\frac{32}{3}} \approx \sqrt{10.67} \approx 3.27 \] 2) For the pair \( 5 \) and \( 10 \): \[ \text{Geometric Mean} = \sqrt{5 \cdot 10} = \sqrt{50} = 5\sqrt{2} \approx 7.07 \] 3) For the single number \( 624 \), since there is no pair, the geometric mean is simply the number itself: \[ \text{Geometric Mean} = 624 \] In summary, the geometric means are: 1) \( \sqrt{\frac{32}{3}} \approx 3.27 \) 2) \( 5\sqrt{2} \approx 7.07 \) 3) \( 624 \)