Question

The square of which of the following numbers would be an odd number?
$3456$

Answer 1

Hint: Here we are asked to find whether the square of the given number is an odd number or not. This can be done in two ways: the first way is finding the square of the given number and seeing whether the square is even or odd and the other way is finding the solution using the properties of the square numbers. We will find the solution to this problem by using properties.

Complete step-by-step answer:
We are given a number that is $3456$ we aim to find whether the square of this number is odd or even.
Before going into the solution of this problem let us first recall some properties of square numbers.
The square of an odd number is always an odd number and the square of the even number is always an even number.
The unit digit of a square of a number is the unit digit of the square of that number’s unit digit.
Now let us get into the solution of this problem. The given number is $3456$ from the unit digit of this number that is $6$ we can say that this is an even number. So, by the property that is given above “The square of an odd number is always an odd number and the square of the even number is always an even number” we can say that the square of the number $3456$ is also not even odd.
Thus, we have the answer that the square of the given number is not odd.
This solution can also be solved by using the other property that is given above.
We know that if the number’s unit digit is odd then it is an odd number and if it is even then it is an even number. So, if we know the unit digit of the square of the given number, we can find whether it is even or odd.
Now let us find the unit digit of the square of the given number. By the second property that is “The unit digit of a square of a number is unit digit of the square of that number’s unit digit” the unit digit of the square of the number $3456$ is
${6^2} = 36$
we got the unit digit of the square of the given number as $6$ which is an even number. From this we can say that the square of the given number is not an odd number.

Note: The above problem can also be done in the following way:
${3456^2} = 3456 \times 3456 = 11943936$
We know that we can check whether the number is odd or even by seeing its unit digit. If the unit digit is even then it is an even number or if the unit digit is odd then it is an odd number. Here we got the unit digit of the square of the given number as $6$ which is an even number thus, the square of the given number is even not odd.