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,
$${26}^2<728<{27}^2$$
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.