Question

What are the perfect square integers between $1$ and $80$ inclusive?

Answer 1

Hint: Here, in the given question, we need to find the perfect square integers between $1$ and $80$ inclusive. Here, $1$ and $80$ inclusive means $1$ and $80$ are included. A square number or perfect square is an integer that is the square of an integer; in other words, it is the product of the same integer itself. As we know that, a negative times a negative is positive, a perfect square is always positive. We will calculate the perfect square integers between $1$ and $80$ inclusive one by one. As we know the square of $10$ is $100$, so we will write squares of all the numbers from $1$ to $9$.

Complete step-by-step answer:
Let us list the squares of all the numbers from $1$ to $9$ to find the perfect square integers between $1$ and $80$ inclusive.
The perfect square of $1$ is:
$ \Rightarrow 1 \times 1 = 1$
The perfect square of $2$ is:
$ \Rightarrow 2 \times 2 = 4$
The perfect square of $3$ is:
$ \Rightarrow 3 \times 3 = 9$
The perfect square of $4$ is:
$ \Rightarrow 4 \times 4 = 16$
The perfect square of $5$ is:
$ \Rightarrow 5 \times 5 = 25$
The perfect square of $6$ is:
$ \Rightarrow 6 \times 6 = 36$
The perfect square of $7$ is:
$ \Rightarrow 7 \times 7 = 49$
The perfect square of $8$ is:
$ \Rightarrow 8 \times 8 = 64$
The perfect square of $9$ is:
$ \Rightarrow 9 \times 9 = 81$
As we can see the square of $9$ is greater than $80$, so we will not include it in our final answer.
Therefore, the perfect square integers between $1$ and $80$ inclusive are $1,4,9,16,25,36,49,64$.
So, the correct answer is “$1,4,9,16,25,36,49,64$”.

Note: Perfect squares are the numbers which we obtain by multiplying any whole number twice. Many students make mistakes by not including $1$, but we need to include it in the answer because it is mentioned in the question that $1$ and $80$ inclusive. Remember that squares of all integers are known as perfect squares.