Using nonperfect square method,find the square root of 418 correct to two decimal places, showing workings.

Answer 1

Newton's method of square root estimation often leads directly to the minimal solution.
1--Make an estimate of the square root of N = n.
2--Then, calculate n1 = [N/n + n]/2
3--For further accuracy, calculate n2 = [N/n1 + n1]/2

Example: Estimate the square root of 73.
n1 = [73/8 + 8]/2 = 8.5625
n2 = [73/8.5625 + 8.5625]/2 = 8.54402
The actural square root of 73 is 8.544003745.
The method gives a reasonably close estimate in two calculations.

Answer 2

squar root of 2.5