Question

What is the perfect square between \[49\] and \[81\]?

Answer 1

Hint: In order to find a square root between \[49\] and \[81\], let us check out if \[49\] and \[81\] are perfect squares, if they are true for the case of perfect squares, we can find out the next perfect square that would occur in the given set.

Complete step by step solution:
Now let us learn more about perfect squares. A perfect square is a perfect square that is generated by multiplying two integers by each other. Square of an even number is always an even number in the same way, the square of an odd number is always an odd number. A perfect square always ends with the digits \[0,1,4,5,6,9\]. If a number has \[n\] zeroes, then its perfect square will have \[2n\] number of zeroes in the end.
Now let us find out if \[49\] and \[81\] are perfect squares or not.
We know that if a number ends with \[0,1,4,5,6,9\] it is a perfect square. So we can say that \[49\] and \[81\], can be perfect squares.
Now let us confirm by checking it out by finding out the square roots of \[49\] and \[81\].
The square root of \[49\] is \[7\].
The square root of \[81\] is \[9\].
Since the given numbers are perfect squares, there exists another perfect square in between the given list as the given numbers are alternate numbers.
The number between \[7\] and \[9\] is \[8\].
The square of \[8\] is \[64\].

\[\therefore \] The perfect square between \[49\] and \[81\] is \[64\].

Note:
A perfect square can have only an even number of zeros at the end. If a number is a perfect square, then it has to be the sum of successive odd numbers starting from \[1\]. If a number is a square of an odd number, then it has to be written as a sum of consecutive numbers.