How do you estimate $\sqrt {35} $ to the nearest integer?

Hint: The art of estimation requires us to first be very good with the value of square or the value of square root. To estimate the given number $\sqrt {35} $ to the nearest integer we will first have to find numbers near it which are perfect squares, then we will have to see our number is nearest to which whole square number then we will find the square root of that particular number and then we will be able to guess the number which our given number is nearest to. The number we obtain will be approximate but that is what we exactly have to do we have to find the nearest integer.

Complete step by step solution:
 The given number under square root sign will be estimated by finding where it lies between the two perfect square as we know the square of $5$is $25$and the square of $6$is $36$our number since it lies between these two numbers either our number will be $5$or $6$. The difference between $25$and $35$is ,
$35 - 25 = 10$,
While the difference between $36$and $35$is ,
$36 - 35 = 1$
Since the difference between $36$and $35$is less, our estimated value of $\sqrt {35} $ is 6 to the nearest integer.

Note: There are many other ways as well by which we estimate the value of an expression but the above method is most suitable for estimating the value of numbers under square root and will serve us well if we know the respective squares of the numbers .