Which is the greatest five-digit number which is a perfect square. Also, find the square root of the number so obtained.

Grade:9

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99999 and 333

99856 and 316

99881 and 319

None if the above

answer is B.

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Detailed Solution

We know that the greatest five-digit natural number is 99999.
Now we will try to evaluate whether 99999 is a perfect square or not.
From the division method of square root evaluation, we get the remainder as 143.
Which implies, 99999 is not a perfect square.
Now, subtracting 143 from 99999 we get,
99999 – 143 = 99856.
So,
99856 is the largest five- digit perfect square number.
For finding the square root of 99856 we could express 99856 in terms of prime factors as 24×792 and then taking the root, we get the square root of 99856 as:
√(2⁴×79²)
=2²×79
=316
So, the largest five-digit perfect square number is 99856 whose square root is 316
Hence , option B) 99856 and 316 is the correct answer.

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