Question

# Find the nearest integer to the square root of $728$.

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.

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.