The least possible number which must be subtracted from 575 to make a perfect square number is :

Options

A. 5
B. 50
C. 46
D. 37

Answer

To find the least possible number that must be subtracted from 575 to make it a perfect square, we can follow these steps:

### Step 1: Identify the nearest perfect squares around 575.
Perfect squares are numbers that can be expressed as the square of an integer. We can find the square roots of numbers around 575 to identify the nearest perfect squares.

- The square root of 575 is approximately 23.9.
- The nearest integers are 23 and 24.
- Therefore, the perfect squares we will consider are:
- \(23^2 = 529\)
- \(24^2 = 576\)

### Step 2: Calculate the differences.
Now, we will calculate how much we need to subtract from 575 to reach these perfect squares.

1. To reach \(23^2 = 529\):
\[ 575 - 529 = 46 \]

2. To reach \(24^2 = 576\):
\[ 576 - 575 = 1 \]

### Step 3: Determine the least number to subtract.
From the calculations above:
- To make 575 a perfect square of 529, we need to subtract 46.
- To make 575 a perfect square of 576, we need to add 1, which is not a subtraction.

Thus, the least number that must be subtracted from 575 to make it a perfect square is **46**.

### Final Answer:
The least possible number which must be subtracted from 575 to make a perfect square number is **46**.

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