The least number which must be added to 1728 to make it a perfect square is ________.

Options

A. 36
B. 32
C. 38
D. 30

Answer

To find the least number that must be added to 1728 to make it a perfect square, we can follow these steps:

### Step 1: Find the square root of 1728
First, we need to determine the square root of 1728 to see if it is already a perfect square or how close it is to one.

\[ \sqrt{1728} \approx 41.57 \]

### Step 2: Identify the next whole number
Since the square root is approximately 41.57, the next whole number is 42.

### Step 3: Calculate the perfect square of the next whole number
Now, we calculate the perfect square of 42.

\[ 42^2 = 1764 \]

### Step 4: Find the difference between 1764 and 1728
Next, we subtract 1728 from 1764 to find the least number that needs to be added.

\[ 1764 - 1728 = 36 \]

### Conclusion
Thus, the least number that must be added to 1728 to make it a perfect square is:

\[ \boxed{36} \]

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