Find the third proportional to :
36, 12

Answer

To find the third proportional to the numbers 36 and 12, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Third Proportional**:
The third proportional to two numbers \( a \) and \( b \) is a number \( x \) such that the ratio \( a:b \) is equal to the ratio \( b:x \). This can be expressed as:
\[ \frac{a}{b} = \frac{b}{x} \]

2. **Setting Up the Equation**:
For our numbers, let \( a = 36 \) and \( b = 12 \). We can set up the equation:
\[ \frac{36}{12} = \frac{12}{x} \]

3. **Cross Multiplying**:
To eliminate the fractions, we can cross-multiply:
\[ 36 \cdot x = 12 \cdot 12 \]

4. **Calculating the Right Side**:
Calculate \( 12 \cdot 12 \):
\[ 12 \cdot 12 = 144 \]
So, we have:
\[ 36x = 144 \]

5. **Solving for \( x \)**:
Now, divide both sides by 36 to solve for \( x \):
\[ x = \frac{144}{36} \]

6. **Simplifying the Fraction**:
Simplify \( \frac{144}{36} \):
\[ x = 4 \]

7. **Conclusion**:
Therefore, the third proportional to 36 and 12 is:
\[ \boxed{4} \]