Question

Find the nearest integer to the square root of \[728\].

Answer 1

Hint: First we will check in between which square values \[728\] lies. Like in this case \[728\] lies between \[{26^2}\] to \[{27^2}\]. Then we will find the difference of the lower number with \[728\] and the higher number with \[728\]. Any one of the cases which gives the lower value that will be the nearest integer.

Complete Answer:
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.

Note: Square root of only positive numbers are defined and for negative number square root is not defined. The positive number might be fractions or decimals.