The least possible number which must be subtracted from 574 to make a perfect square number is :

Options

A. 5
B. 50
C. 45
D. 37

Answer

To find the least possible number that must be subtracted from 574 to make it a perfect square, we can follow these steps:

### Step 1: Identify the nearest perfect square
First, we need to find the perfect square that is closest to 574. We can do this by calculating the square root of 574.

\[ \sqrt{574} \approx 23.98 \]

### Step 2: Calculate the perfect squares around this value
Next, we find the perfect squares of the integers around 23.98, which are 23 and 24.

\[ 23^2 = 529 \]
\[ 24^2 = 576 \]

### Step 3: Determine the differences
Now, we calculate how much we need to subtract from 574 to reach these perfect squares.

1. To reach 529:
\[ 574 - 529 = 45 \]

2. To reach 576:
\[ 576 - 574 = 2 \]

### Step 4: Identify the least number to subtract
From the calculations above, we see that to reach the perfect square 529, we need to subtract 45, and to reach 576, we would need to add 2. Since we are looking for the least number to subtract, we choose 45.

### Conclusion
Thus, the least possible number that must be subtracted from 574 to make it a perfect square is:

\[ \boxed{45} \]

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