Question

The Square of which of the following numbers will be an odd number?
A.$431$
B.$2826$
C.$7779$
D.$82004$

Answer 1

Hint: It is always required to check the unit’s place digit in case of an odd or even number. Also, during the squaring process the unit's place digit should be multiplied by itself and the number obtained in the unit’s place should be considered for deciding the odd or even number.


Complete step-by-step answer:
$431$
The number $431$ is an odd number and contains $1$ at its unit place.
If the squaring of this odd number is done then at the unit’s place $1$ is multiplied by $1$ will give $1$ at the unit’s place of the squared term and $1$ is an odd number.
Thus, the square of $431$ is an odd number.

$2826$
The number $2826$ is an even number and contains $6$ at its unit place.
If the squaring of this even number is done then at the unit’s place $6$ is multiplied by $6$ will give $6$ at the unit’s place of the squared term$\left( {6 \times 6 = 36} \right)$ and $6$ is an even number.
Thus, the square of $2826$ is an even number.

$7779$
The number $7779$ is an odd number and contains $9$ at its unit place.
If the squaring of this even number is done then at the unit’s place $9$ is multiplied by $9$ will give at the unit’s place of the squared term. $\left( {9 \times 9 = 81} \right)$and $1$ is an odd number.
Thus, the square of $7779$ is an odd number.

$82004$
The number $82004$ is an even number and contains $4$ at its unit place.
If the squaring of this even number is done then at the unit’s place $4$ is multiplied by $4$ will give $6$ at the unit’s place of the squared term. $\left( {4 \times 4 = 16} \right)$and $6$ is an even number.
Thus, the square of $82004$ is an even number.


Note: The above problem can also be solved by this logic that the square of an even number is always an even number and the square of an odd number will always be an odd number.
 The number is even and odd, it is decided based on its unit’s place digit only.