G.M. Between a and b is equal to………………….

Answer

To find the geometric mean (G.M.) between two numbers \( a \) and \( b \), we can follow these steps:

### Step-by-Step Solution:

1. **Define the Geometric Mean**:
We denote the geometric mean between \( a \) and \( b \) as \( G \).

2. **Establish the Relationship**:
Since \( a \), \( G \), and \( b \) are in geometric progression, we can use the property of geometric progression which states that the ratio of consecutive terms is constant. Thus, we have:
\[ \frac{G}{a} = \frac{b}{G} \]

3. **Cross Multiply**:
To eliminate the fractions, we cross-multiply:
\[ G^2 = a \cdot b \]

4. **Solve for G**:
To find \( G \), we take the square root of both sides:
\[ G = \sqrt{a \cdot b} \]

5. **Final Result**:
Therefore, the geometric mean between \( a \) and \( b \) is:
\[ G = \sqrt{a \cdot b} \]

### Conclusion:
The geometric mean between \( a \) and \( b \) is equal to \( \sqrt{a \cdot b} \).

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