Find the least number that must be subtracted from 50730 to make it a perfect square.

Options

A. 205
B. 105
C. 110
D. None of these

Answer

To find the least number that must be subtracted from 50730 to make it a perfect square, we can follow these steps:

### Step 1: Find the square root of 50730
First, we need to determine the approximate square root of 50730. We can do this by finding the nearest perfect squares.

- The square of 225 is \( 225^2 = 50625 \).
- The square of 226 is \( 226^2 = 51076 \).

Since \( 50625 < 50730 < 51076 \), we know that the square root of 50730 is between 225 and 226.

### Step 2: Calculate the nearest perfect square
The nearest perfect square less than 50730 is \( 50625 \) (which is \( 225^2 \)).

### Step 3: Find the difference
Now, we need to find the difference between 50730 and 50625:

\[ 50730 - 50625 = 105 \]

### Conclusion
The least number that must be subtracted from 50730 to make it a perfect square is **105**.

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