Question

Find the perfect square numbers between
(i) 30 and 40
(ii) 50 and 60.

Answer 1

Hint: Here we will write the square of each of the numbers starting from 1 and then check which numbers lie in the given intervals to get the desired square numbers.

Complete step-by-step answer:
(i) Here we have to find the perfect square numbers between 30 and 40.
We will write the squares of each number starting from 1.
So let us first write the square of 1:-
\[1 \times 1 = 1\]
Now since 1 does not lie in the interval of 30 and 40.
Hence we will now write the square of 2:-
\[2 \times 2 = 4\]
Now since 4 does not lie in the interval of 30 and 40.
Hence we will now write the square of 3:-
\[3 \times 3 = 9\]
Now since 9 does not lie in the interval of 30 and 40.
Hence we will now write the square of 4:-
\[4 \times 4 = 16\]
Now since 16 does not lie in the interval of 30 and 40.
Hence we will now write the square of 5:-
\[5 \times 5 = 25\]
Now since 25 does not lie in the interval of 30 and 40.
Hence we will now write the square of 6:-
\[6 \times 6 = 36\]
Now 36 lies between 30 and 40.
Hence 36 is the required square number between 36 and 40.
Now let us consider part (ii).
(ii) Here we have to find the perfect square numbers between 50 and 60.
We will write the squares of each number starting from 1.
So let us first write the square of 1:-
\[1 \times 1 = 1\]
Now since 1 does not lie in the interval of 50 and 60.
Hence we will now write the square of 2:-
\[2 \times 2 = 4\]
Now since 4 does not lie in the interval of 50 and 60.
Hence we will now write the square of 3:-
\[3 \times 3 = 9\]
Now since 9 does not lie in the interval of 50 and 60.
Hence we will now write the square of 4:-
\[4 \times 4 = 16\]
Now since 16 does not lie in the interval of 50 and 60.
Hence we will now write the square of 5:-
\[5 \times 5 = 25\]
Now since 25 does not lie in the interval of 50 and 60.
Hence we will now write the square of 6:-
\[6 \times 6 = 36\]
Now since 36 does not lie in the interval of 50 and 60.
Hence we will now write the square of 7:-
\[7 \times 7 = 49\]
Now since 49 does not lie in the interval of 50 and 60.
Hence we will now write the square of 8:-
\[8 \times 8 = 64\]
Since 64 does not lie in the interval of 50 and 60.
Hence, there is no square number between 50 and 60.

Note: Students should note that a square number is a product of a number multiplied by itself.
Also, students should stop writing the square numbers once they find a number that lies between the given interval.