Question

Is $100$ a perfect square?

Answer 1

Hint : A perfect square is nothing but a number that can be expressed as the product of two equal integers (i.e.) it is a number obtained by multiplying two equal numbers with one another.
Now, we shall learn the steps that are to be followed to find the number that is a perfect square.
A perfect square number never ends with the digits $2,3,7or8$ . If the given number ends with one of these digits, it can’t be a perfect square number.
We need to find the digital root of the given number. The sum of all the digits of the number is said to be the digital root. Because a perfect square number contains a digital root $1,4,7,9$ .

Complete step-by-step solution:
The given number is $100$.
We are asked to find whether the given number is a perfect square or not.
a) The first step is to find the given number whether it ends with $2,3,7or8$ .
Here, $100$ ends with zero. Thus, we can move to the next step.
b) The second step is to find the digital roots of the given number. The sum of all the digits of the number is said to be the digital root.
Here,\[100 = 1 + 0 + 0 = 1\]
Hence $1$ is the digital root of the given number.
Since the given number contains the digital root $1$ , we can conclude that $100$ is a perfect square number.
Next, we shall find all the factors of $100$.
$100 = 1 \times 100$ ,
$100 = 2 \times 50$ ,
$100 = 4 \times 25$ ,
$100 = 5 \times 20$ ,
$100 = 10 \times 10$
A number that consists of a product of two equal integers is known as a perfect square.
Since $100 = 10 \times 10$ we can conclude that $100$ is a perfect square number.

Note: We are asked to find whether the given number is a perfect square or not.
a) The first step is to find the given number whether it ends with $2,3,7or8$ .
b) The second step is to find the digital roots of the given number. The sum of all the digits of the number is said to be the digital root.