By which least number should 5000 be divided so that it becomes a perfect square ?

Options

A. 2
B. 5
C. 10
D. 25

Answer

To determine the least number by which 5000 should be divided to become a perfect square, we can follow these steps:

### Step 1: Prime Factorization of 5000
First, we need to find the prime factorization of 5000.

5000 can be expressed as:
\[ 5000 = 5^4 \times 2^3 \]

### Step 2: Understanding Perfect Squares
A number is a perfect square if all the powers in its prime factorization are even.

### Step 3: Analyze the Factorization
From the factorization \( 5^4 \times 2^3 \):
- The power of 5 is 4 (which is even).
- The power of 2 is 3 (which is odd).

### Step 4: Making Powers Even
To make the power of 2 even, we need to reduce it by 1 (since 3 is odd). This means we need to divide by \( 2^1 \) (which is 2).

### Step 5: Calculate the Result
Now, we divide 5000 by 2:
\[ \frac{5000}{2} = 2500 \]

### Step 6: Verify if 2500 is a Perfect Square
Next, we check if 2500 is a perfect square:
\[ 2500 = 50^2 \]
Since 50 is an integer, 2500 is indeed a perfect square.

### Conclusion
The least number by which 5000 should be divided to become a perfect square is **2**.

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