Find the third proportional of 6 and 30.

Answer

To find the third proportional of 6 and 30, we can follow these steps:

### Step 1: Understand 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 the same as the ratio \( b:x \).

### Step 2: Set up the proportion
Given the numbers 6 and 30, we can express this relationship as:
\[ \frac{6}{30} = \frac{30}{x} \]

### Step 3: Cross-multiply to eliminate the fractions
Cross-multiplying gives us:
\[ 6 \cdot x = 30 \cdot 30 \]

### Step 4: Calculate the right-hand side
Calculate \( 30 \cdot 30 \):
\[ 30 \cdot 30 = 900 \]
So, we have:
\[ 6x = 900 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 6 to find \( x \):
\[ x = \frac{900}{6} \]

### Step 6: Perform the division
Calculating \( \frac{900}{6} \):
\[ x = 150 \]

### Conclusion
Thus, the third proportional of 6 and 30 is \( 150 \).

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