The smallest number that must be subtracted from 1000 to make the resulting number a perfect square is

Options

A. 37
B. 38
C. 39
D. 40

Answer

To find the smallest number that must be subtracted from 1000 to make the resulting number a perfect square, we can follow these steps:

### Step 1: Identify the nearest perfect square less than 1000
We need to find the largest integer whose square is less than 1000. To do this, we can calculate the square root of 1000.

\[ \sqrt{1000} \approx 31.62 \]

### Step 2: Find the perfect square
The largest integer less than 31.62 is 31. Now, we calculate the square of 31.

\[ 31^2 = 961 \]

### Step 3: Subtract the perfect square from 1000
Now, we subtract this perfect square (961) from 1000 to find the smallest number that must be subtracted.

\[ 1000 - 961 = 39 \]

### Conclusion
The smallest number that must be subtracted from 1000 to make the resulting number a perfect square is **39**.

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