The following algorithm finds the square root of a positive number:
Algorithm squareRoot(number, lowGuess, highGuess, tolerance)
newGuess = (lowGuess + highGuess) / 2
if ((highGuess - newGuess) / newGuess
return newGuess
else if (newGuess * newGuess > number)
return squareRoot(number, lowGuess, newGuess, tolerance)
else if (newGuess * newGuess
return squareRoot(number, newGuess, highGuess, tolerance)
else
return newGuess
To begin the computation, you need a value lowGuess that is less than the square root of the number and a value highGuess that is larger. You can use zero as lowGuess and the number itself as highGuess. The parameter tolerance controls the precision of the result independently of the magnitude of number. For example, computing the square root of 250 with tolerance equal to 0.00005 results in 15.81. This result has four digits of accuracy. Implement this algorithm.