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Q.

What will be the value of the square 999 2  ?


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a

999001

b

998001

c

997001

d

996001 

answer is B.

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Detailed Solution

The given square number is 999 2 .  
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.
∴ 999 2 = 1000−1 2  
Apply the algebraic identity,
a−b 2 = a 2 + b 2 −2ab  
∴ 999 2 = 1000−1 2 ⇒ 999 2 = 1000 2 + 1 2 −2×1000×1 ⇒ 999 2 =1000000+1−2000 ⇒ 999 2 =998001.  
Therefore, the value of the square 999 2 =998001.  
Hence, option (2) is correct.
 
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