Find the greatest 4-digit number which is a perfect square.a)9990b)9801c)9999d)none of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

By division method we find the root of 9999 and we get the remainder 198.So subtracting 198 from 9999 we get 9801 as the greatest 4-digit perfect square.

Answer

Answer is b

Answer

Explanation:

To find the greatest 4-digit number which is a perfect square, we need to consider the perfect squares between 1000 and 9999.

Finding the perfect squares:
To find the perfect squares between 1000 and 9999, we can start by finding the square root of the lower and upper limits.

The square root of 1000 is approximately 31.62 and the square root of 9999 is approximately 99.99.

Therefore, we need to find the perfect squares between 31.62 and 99.99.

Finding the perfect squares within the given range:
Starting from the square root of the lower limit (31.62), we can incrementally find the perfect squares within the given range.

31.62 * 31.62 = 999.4244 (not a perfect square)
32 * 32 = 1024 (not within the given range)

Continuing this process, we find that the square root of 9801 is approximately 99.00499, which is within the given range.

Verifying the answer:
To verify if 9801 is a perfect square, we can take its square root.

√9801 ≈ 99.00499

Since the square root of 9801 is approximately 99.00499, we can conclude that 9801 is a perfect square.

Conclusion:
The greatest 4-digit number which is a perfect square is 9801. Therefore, the correct answer is option B.

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