Question

9 is the geometric mean between 4 and which other number?
20.25
81
9
none of the choices are correct.

Explanation:

Step1: Recall geometric mean formula

The geometric mean \( g \) between two numbers \( a \) and \( b \) is given by \( g = \sqrt{ab} \). Here, \( g = 9 \) and \( a = 4 \), we need to find \( b \).

Step2: Solve for \( b \)

From \( g=\sqrt{ab} \), square both sides: \( g^{2}=ab \). Substitute \( g = 9 \) and \( a = 4 \): \( 9^{2}=4\times b \) → \( 81 = 4b \). Then \( b=\frac{81}{4}=20.25 \).

Answer:

20.25 (corresponding to the first option with the dotted circle, so the option is "20.25")