Below is a Python script that approximates the positive square root of positive integers. The algorithm makes guesses by continually averaging the upper and lower bound of a range of numbers that dynamically adjusts.

## Number we seek the sqrt ofn=input("Find sqrt of: ")## input() gets input from the console## Set the boundsupperBound=nlowerBound=0## Acceptable variation in resultdelta=0.00001## Current guess at sqrt of nguess=(upperBound+lowerBound)/2.0## Checks if guess*guess is within +/- delta of nwhileguess*guess<n-deltaorguess*guess>n+delta:## Resets bounds according to outcomeifguess**2<n-delta:lowerBound=guesselse:upperBound=guessguess=(upperBound+lowerBound)/2.0test=int(guess+0.5)## int() casts other number types into integersiftest**2==n:guess=testprintguess

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