Finding the Smallest Number to Subtract for a Perfect Square
The objective is to find the smallest number that, when subtracted from 63535, results in a perfect square.
Step 1: Calculate the Square Root
First, find the square root of the given number, 63535.
$ \sqrt{63535} \approx 252.0616 $
Step 2: Identify the Integer Part
The integer part of the square root is 252. This represents the largest integer whose square is less than or equal to 63535.
Step 3: Calculate the Largest Perfect Square
Square the integer part found in Step 2 to determine the largest perfect square less than 63535.
$ 252^2 = 63504 $
Step 4: Determine the Number to Subtract
Subtract the largest perfect square (calculated in Step 3) from the original number (63535) to find the smallest number that needs to be subtracted.
$ \text{Number to subtract} = 63535 - 63504 $
$ \text{Number to subtract} = 31 $
Conclusion
Subtracting 31 from 63535 gives 63504, which is a perfect square ($252^2$). Therefore, 31 is the smallest number that must be subtracted.
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Which of the above statements is/are correct ?
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