The Geometric Mean (GM) of $4$ and $9$ is

1. GM of two positive numbers $a, b$: $\text{GM} = \sqrt{ab}$. 2. Plug in $a = 4$, $b = 9$: $\text{GM} = \sqrt{36} = 6$. 3. Note: AM = $(4+9)/2 = 6.5$ and HM = $2\cdot 4 \cdot 9 / 13 = 72/13 \approx 5.54$. So AM > GM > HM (always true for distinct positives). 4. Option A is the AM (confusing the two). Option B is the HM (off but close). Option D is the PRODUCT $a \cdot b$ (forgot to take the root). _Source: NCERT Class 11 Mathematics, Ch 8, §8.4 (Geometric Mean), p. 10._