Mean proportional between 17 and 153 is :

Options

A. 51
B. 24
C. 4
D. 34

Answer

To find the mean proportional between 17 and 153, we can follow these steps:

### Step 1: Set up the proportion
Let the mean proportional be \( x \). According to the definition of mean proportional, we have:
\[ \frac{17}{x} = \frac{x}{153} \]

### Step 2: Cross-multiply
Cross-multiplying gives us:
\[ 17 \cdot 153 = x \cdot x \]
This simplifies to:
\[ x^2 = 17 \cdot 153 \]

### Step 3: Calculate \( 17 \cdot 153 \)
Now we need to calculate \( 17 \cdot 153 \):
\[ 17 \cdot 153 = 2601 \]

### Step 4: Solve for \( x \)
Now, we take the square root of both sides to find \( x \):
\[ x = \sqrt{2601} \]

### Step 5: Simplify \( \sqrt{2601} \)
To simplify \( \sqrt{2601} \), we can factor it:
\[ \sqrt{2601} = \sqrt{17 \cdot 153} = \sqrt{17 \cdot 17 \cdot 9} = \sqrt{17^2 \cdot 9} = 17 \cdot 3 = 51 \]

### Final Answer
Thus, the mean proportional between 17 and 153 is:
\[ \boxed{51} \]

---