There are several techniques for implementing the sqrt function as found in the

ID: 3551632 • Letter: T

Question

There are several techniques for implementing the sqrt function as found in the cmath

header. One such technique is known as the Babylonian method.

1 It approximates the square

root of a number, num, by repeatedly performing a calculation using the following formula:

nextGuess = ( lastGuess + num / lastGuess ) / 2;

When nextGuess and lastGuess are almost identical, nextGuess is the approximated

square root. The initial guess can be any positive value (e.g., 1). This value will be the

starting value for lastGuess. If the difference between nextGuess and lastGuess is

less than a very small number, such as 0.000001, you can claim that nextGuess is the

approximated square root of num. If not, nextGuess becomes lastGuess and the

approximation process continues.

Implement functions from the following prototypes:

// returns the square root of num

double squareRoot( double num );

// returns the absolute value of num

void absoluteValue( double& num );

// neatly prints a table of values and their square roots

void printTable( ofstream& ofs, int begin, int end, int step );

Write a program (pa05.cpp) that prints the following table formatted exactly as shown

below. Your output should be saved to a file named output.txt:

Number SquareRoot

------ ----------

0 0.0000

2 1.4142

...

48 6.9282

50 7.0711