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What will be the value of the square $9992$ ?

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999001

998001

997001

996001

answer is B.

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Detailed Solution

The given square number is

9992 .

To avoid a lengthy calculation, it is better to divide the three-digit number into its simplest form and then expand the bracket using the algebraic identity.

∴ 9992 = 1000 − 1 2

Apply the algebraic identity,

a − b 2 = a 2 + b 2 − 2 a b

∴ 9992 = 1000 − 1 2 ⇒ 9992 = 10002 + 12 − 2 × 1000 × 1 ⇒ 9992 = 1000000 + 1 − 2000 ⇒ 9992 = 998001.

Therefore, the value of the square

9992 = 998001.

Hence, option (2) is correct.

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