Describe how you would estimate the square root of a number that is not a perfect square without using a calculator. lets say n was the imperfect square number and the square root is w. the square root of n = n+w squared/ 2w.

To get the square root of imperfect square we can use the formula , which is usually accurate to about two decimal places,
√X =√S +(X-S)2√S
Where, X = the number you want the square roof of, and S is the closest square you know to x.
For example 75 is an imperfect square
Thus, X=75 and thus the nearest number S = 81, this ,means √81 =9.
Putting this into the formula;
√75= 9+(75-81)/2/2(9)
      =  9 + -6/18 
      = 9-0.33333 = 8.667
= 8.667, thus the square root of 75 is 8.66