What is the least number which must be added to 306452 that make it a perfect square ?

Options

A. 460
B. 462
C. 464
D. 466

Answer

To determine the least number that must be added to 306452 to make it a perfect square, we can follow these steps:

### Step 1: Find the square root of 306452
We first need to calculate the square root of 306452.

Using a calculator or estimation, we find:
\[ \sqrt{306452} \approx 553.5 \]

### Step 2: Determine the nearest whole number
Since we need a perfect square, we consider the nearest whole numbers to 553.5, which are 553 and 554.

### Step 3: Calculate the squares of these whole numbers
Now we calculate the squares of 553 and 554:
- For 553:
\[ 553^2 = 305809 \]
- For 554:
\[ 554^2 = 306916 \]

### Step 4: Find the difference between 306452 and these squares
Next, we find the differences:
- Difference with 305809:
\[ 306452 - 305809 = 643 \]
- Difference with 306916:
\[ 306916 - 306452 = 464 \]

### Step 5: Determine the least number to be added
Now, we need to find the least number that must be added to 306452 to make it a perfect square. We compare the differences:
- To reach 305809, we need to add 643.
- To reach 306916, we need to add 464.

The least number to be added is:
\[ \text{Least number} = 464 \]

### Final Answer
Thus, the least number which must be added to 306452 to make it a perfect square is **464**.

---