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What is the greatest five-digit number that is a perfect square?

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999856

999876

998796

999874

answer is A.

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Detailed Solution

It is required to find the greatest five-digit number that is a perfect square.
We know that 99999 is the largest five-digit number.
The long division approach yields the square of 99999,
Question Image

Clearly,

3162 < 99999 < 3172

To obtain the largest possible five digits, which is a square,

99999 − 3162 = 99999 − 99856 ⇒ 43

Consequently, the largest five-digit number that can be expressed as a square,

\Rightarrow

99999 – 43 = 99856
The largest five-digit number that is a perfect square is 999856.
Therefore, option 1 is correct.

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