The product of two positive integers is 2048 and one of them is twice the other. The smaller number is

Options

A. 32
B. 64
C. 16
D. 1024

Answer

To solve the problem, we need to find two positive integers whose product is 2048, and one of them is twice the other. Let's denote the smaller number as \( x \). Therefore, the larger number can be represented as \( 2x \).

### Step-by-step Solution:

1. **Set up the equation**:
Since the product of the two numbers is 2048, we can write the equation:
\[ x \cdot (2x) = 2048 \]

2. **Simplify the equation**:
This simplifies to:
\[ 2x^2 = 2048 \]

3. **Divide both sides by 2**:
To isolate \( x^2 \), divide both sides by 2:
\[ x^2 = \frac{2048}{2} = 1024 \]

4. **Take the square root**:
Now, we find \( x \) by taking the square root of both sides:
\[ x = \sqrt{1024} \]

5. **Calculate the square root**:
The square root of 1024 is:
\[ x = 32 \]

6. **Identify the smaller number**:
Since \( x \) is the smaller number, we conclude that the smaller number is:
\[ \text{Smaller number} = 32 \]

### Final Answer:
The smaller number is **32**.