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First we will find the values of squares in between \[728\] lies

The value of is \[{26^2}\] equal to \[676\]

The value of \[{27^2}\] is equal to \[729\]

And \[728\] is lies between \[676\] and \[729\]

i.e.

\[676 < 728 < 729\]

Or,

\[{26^2} < {\text{ }}728{\text{ }} < {27^2}\]

Now we will calculate the difference of \[676\] and \[728\]

=\[728 - 676\]

=\[52\]

Now find the difference of \[729\] and \[728\]

=\[729 - 728\]

=1

We see one of the differences is \[52\] whereas another is 1.

Therefore the square root of \[728\] is nearest to the integer \[27\]

Hence, the answer is \[27\].

Additional information: In mathematics, a square root of a number x is a number r such that $r^2$ = x.

For example:

1. The square root of 25 is 5 because \[{5^2} = 25\].

2. The square root of 2 is \[1.41421356237\] approximately.

3. The square root of pi (π) is \[1.77245385102\] approximately.